Mixing
How to solve $3^x=3-x$
up vote
1
down vote
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Is it possible to solve for $$3^x=3-x$$ without graphing it?
This question is in the section: Solving Exponential equations in my math textbook.
I have tried to log both sides and solve for it however that just leads me back to the original equation.
algebra-precalculus logarithms exponential-function
asked 14 hours ago
warjwar8
223
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warjwar8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
up vote
1
down vote
favorite
Is it possible to solve for $$3^x=3-x$$ without graphing it?
This question is in the section: Solving Exponential equations in my math textbook.
I have tried to log both sides and solve for it however that just leads me back to the original equation.
algebra-precalculus logarithms exponential-function
asked 14 hours ago
warjwar8
223
New contributor
warjwar8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
14 hours ago
Thank you sir. I like your feedback. Pardon me if I did not follow format, english is not my first language. I hope sir you understand.
– warjwar8
13 hours ago
Have you tried to solve $3^x + x = 3$?
– Robert Soupe
5 hours ago
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Is it possible to solve for $$3^x=3-x$$ without graphing it?
This question is in the section: Solving Exponential equations in my math textbook.
I have tried to log both sides and solve for it however that just leads me back to the original equation.
algebra-precalculus logarithms exponential-function
asked 14 hours ago
warjwar8
223
New contributor
warjwar8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Is it possible to solve for $$3^x=3-x$$ without graphing it?
This question is in the section: Solving Exponential equations in my math textbook.
I have tried to log both sides and solve for it however that just leads me back to the original equation.
algebra-precalculus logarithms exponential-function
algebra-precalculus logarithms exponential-function
asked 14 hours ago
warjwar8
223
New contributor
warjwar8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 14 hours ago
warjwar8
223
New contributor
warjwar8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 14 hours ago
asked 14 hours ago
warjwar8
223
New contributor
warjwar8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 14 hours ago
warjwar8
223
asked 14 hours ago
warjwar8
223
223
New contributor
warjwar8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
warjwar8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
warjwar8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
14 hours ago
Thank you sir. I like your feedback. Pardon me if I did not follow format, english is not my first language. I hope sir you understand.
– warjwar8
13 hours ago
Have you tried to solve $3^x + x = 3$?
– Robert Soupe
5 hours ago
add a comment |
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
14 hours ago
Thank you sir. I like your feedback. Pardon me if I did not follow format, english is not my first language. I hope sir you understand.
– warjwar8
13 hours ago
Have you tried to solve $3^x + x = 3$?
– Robert Soupe
5 hours ago
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
14 hours ago
Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
14 hours ago
Thank you sir. I like your feedback. Pardon me if I did not follow format, english is not my first language. I hope sir you understand.
– warjwar8
13 hours ago
Thank you sir. I like your feedback. Pardon me if I did not follow format, english is not my first language. I hope sir you understand.
– warjwar8
13 hours ago
Have you tried to solve $3^x + x = 3$?
– Robert Soupe
5 hours ago
Have you tried to solve $3^x + x = 3$?
– Robert Soupe
5 hours ago
add a comment |
2 Answers
2
active
oldest
votes
up vote
1
down vote
HINT
Let consider
$$f(x)=3^x-(3-x)$$
and note that
- $f(0)=-2$
- $f(1)=1$
therefore by IVT there is a solution in $(0,1)$.
Can you show that this is the unique solution?
answered 14 hours ago
gimusi
85.5k74293
If I am correct then: for $x>1$ the term $3^x +x$ is more positive than '3' everywhere in that domain. Also, for x<0 the term $-3+x$ is more negative to be neutralized by $3^x$ as $3^x$ will then become in postive fraction number.
– jayant98
13 hours ago
1
@jayant98 We can consider the sign of $f'(x)=3^x log 3 +1$.
– gimusi
13 hours ago
1
Yes Sir! Another way which is more simple and effective.
– jayant98
13 hours ago
@jayant98 Call me simply gimusi! Bye
– gimusi
13 hours ago
add a comment |
up vote
1
down vote
Sure. The solution can be expressed in terms of the Lambert W function. In general, graphing is not a way of "solving" an equation because it cannot give you an exact solution. Graphing the equations above will help you approximate $x approx 0.742$ but cannot give you an exact value.
answered 14 hours ago
Mason
1,6401325
add a comment |
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
HINT
Let consider
$$f(x)=3^x-(3-x)$$
and note that
- $f(0)=-2$
- $f(1)=1$
therefore by IVT there is a solution in $(0,1)$.
Can you show that this is the unique solution?
answered 14 hours ago
gimusi
85.5k74293
If I am correct then: for $x>1$ the term $3^x +x$ is more positive than '3' everywhere in that domain. Also, for x<0 the term $-3+x$ is more negative to be neutralized by $3^x$ as $3^x$ will then become in postive fraction number.
– jayant98
13 hours ago
1
@jayant98 We can consider the sign of $f'(x)=3^x log 3 +1$.
– gimusi
13 hours ago
1
Yes Sir! Another way which is more simple and effective.
– jayant98
13 hours ago
@jayant98 Call me simply gimusi! Bye
– gimusi
13 hours ago
add a comment |
up vote
1
down vote
HINT
Let consider
$$f(x)=3^x-(3-x)$$
and note that
- $f(0)=-2$
- $f(1)=1$
therefore by IVT there is a solution in $(0,1)$.
Can you show that this is the unique solution?
answered 14 hours ago
gimusi
85.5k74293
If I am correct then: for $x>1$ the term $3^x +x$ is more positive than '3' everywhere in that domain. Also, for x<0 the term $-3+x$ is more negative to be neutralized by $3^x$ as $3^x$ will then become in postive fraction number.
– jayant98
13 hours ago
1
@jayant98 We can consider the sign of $f'(x)=3^x log 3 +1$.
– gimusi
13 hours ago
1
Yes Sir! Another way which is more simple and effective.
– jayant98
13 hours ago
@jayant98 Call me simply gimusi! Bye
– gimusi
13 hours ago
add a comment |
up vote
1
down vote
up vote
1
down vote
HINT
Let consider
$$f(x)=3^x-(3-x)$$
and note that
- $f(0)=-2$
- $f(1)=1$
therefore by IVT there is a solution in $(0,1)$.
Can you show that this is the unique solution?
answered 14 hours ago
gimusi
85.5k74293
HINT
Let consider
$$f(x)=3^x-(3-x)$$
and note that
- $f(0)=-2$
- $f(1)=1$
therefore by IVT there is a solution in $(0,1)$.
Can you show that this is the unique solution?
answered 14 hours ago
gimusi
85.5k74293
answered 14 hours ago
gimusi
85.5k74293
answered 14 hours ago
gimusi
85.5k74293
answered 14 hours ago
gimusi
85.5k74293
85.5k74293
If I am correct then: for $x>1$ the term $3^x +x$ is more positive than '3' everywhere in that domain. Also, for x<0 the term $-3+x$ is more negative to be neutralized by $3^x$ as $3^x$ will then become in postive fraction number.
– jayant98
13 hours ago
1
@jayant98 We can consider the sign of $f'(x)=3^x log 3 +1$.
– gimusi
13 hours ago
1
Yes Sir! Another way which is more simple and effective.
– jayant98
13 hours ago
@jayant98 Call me simply gimusi! Bye
– gimusi
13 hours ago
add a comment |
If I am correct then: for $x>1$ the term $3^x +x$ is more positive than '3' everywhere in that domain. Also, for x<0 the term $-3+x$ is more negative to be neutralized by $3^x$ as $3^x$ will then become in postive fraction number.
– jayant98
13 hours ago
1
@jayant98 We can consider the sign of $f'(x)=3^x log 3 +1$.
– gimusi
13 hours ago
1
Yes Sir! Another way which is more simple and effective.
– jayant98
13 hours ago
@jayant98 Call me simply gimusi! Bye
– gimusi
13 hours ago
If I am correct then: for $x>1$ the term $3^x +x$ is more positive than '3' everywhere in that domain. Also, for x<0 the term $-3+x$ is more negative to be neutralized by $3^x$ as $3^x$ will then become in postive fraction number.
– jayant98
13 hours ago
If I am correct then: for $x>1$ the term $3^x +x$ is more positive than '3' everywhere in that domain. Also, for x<0 the term $-3+x$ is more negative to be neutralized by $3^x$ as $3^x$ will then become in postive fraction number.
– jayant98
13 hours ago
1
1
@jayant98 We can consider the sign of $f'(x)=3^x log 3 +1$.
– gimusi
13 hours ago
@jayant98 We can consider the sign of $f'(x)=3^x log 3 +1$.
– gimusi
13 hours ago
1
1
Yes Sir! Another way which is more simple and effective.
– jayant98
13 hours ago
Yes Sir! Another way which is more simple and effective.
– jayant98
13 hours ago
@jayant98 Call me simply gimusi! Bye
– gimusi
13 hours ago
@jayant98 Call me simply gimusi! Bye
– gimusi
13 hours ago
add a comment |
up vote
1
down vote
Sure. The solution can be expressed in terms of the Lambert W function. In general, graphing is not a way of "solving" an equation because it cannot give you an exact solution. Graphing the equations above will help you approximate $x approx 0.742$ but cannot give you an exact value.
answered 14 hours ago
Mason
1,6401325
add a comment |
up vote
1
down vote
Sure. The solution can be expressed in terms of the Lambert W function. In general, graphing is not a way of "solving" an equation because it cannot give you an exact solution. Graphing the equations above will help you approximate $x approx 0.742$ but cannot give you an exact value.
answered 14 hours ago
Mason
1,6401325
add a comment |
up vote
1
down vote
up vote
1
down vote
Sure. The solution can be expressed in terms of the Lambert W function. In general, graphing is not a way of "solving" an equation because it cannot give you an exact solution. Graphing the equations above will help you approximate $x approx 0.742$ but cannot give you an exact value.
answered 14 hours ago
Mason
1,6401325
Sure. The solution can be expressed in terms of the Lambert W function. In general, graphing is not a way of "solving" an equation because it cannot give you an exact solution. Graphing the equations above will help you approximate $x approx 0.742$ but cannot give you an exact value.
answered 14 hours ago
Mason
1,6401325
answered 14 hours ago
Mason
1,6401325
answered 14 hours ago
Mason
1,6401325
answered 14 hours ago
Mason
1,6401325
1,6401325
add a comment |
add a comment |
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warjwar8 is a new contributor. Be nice, and check out our Code of Conduct.
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Welcome to MSE. It will be more likely that you will get an answer if you show us that you made an effort. This should be added to the question rather than in the comments.
– José Carlos Santos
14 hours ago
Thank you sir. I like your feedback. Pardon me if I did not follow format, english is not my first language. I hope sir you understand.
– warjwar8
13 hours ago
Have you tried to solve $3^x + x = 3$?
– Robert Soupe
5 hours ago