Mixing
How to reach this step?
$begingroup$
I failed to understand how the book reached the step with the red border. So any help?
I know that maybe we need to multiply both sides with $ln$ but where did the $e$ go?
Thanks in advance.
logarithms exponential-function
asked Jan 2 at 17:41
Bashayer NouriBashayer Nouri
2018
$endgroup$
add a comment |
$begingroup$
I failed to understand how the book reached the step with the red border. So any help?
I know that maybe we need to multiply both sides with $ln$ but where did the $e$ go?
Thanks in advance.
logarithms exponential-function
asked Jan 2 at 17:41
Bashayer NouriBashayer Nouri
2018
$endgroup$
1
$begingroup$
They have not multiplied by $ln$, they have taken the natural log of both the sides
$endgroup$
– Shubham Johri
Jan 2 at 17:45
$begingroup$
ohh okkk, thank you so much, I appreciate your comment a lot.
$endgroup$
– Bashayer Nouri
Jan 2 at 17:54
add a comment |
$begingroup$
I failed to understand how the book reached the step with the red border. So any help?
I know that maybe we need to multiply both sides with $ln$ but where did the $e$ go?
Thanks in advance.
logarithms exponential-function
asked Jan 2 at 17:41
Bashayer NouriBashayer Nouri
2018
$endgroup$
I failed to understand how the book reached the step with the red border. So any help?
I know that maybe we need to multiply both sides with $ln$ but where did the $e$ go?
Thanks in advance.
logarithms exponential-function
logarithms exponential-function
asked Jan 2 at 17:41
Bashayer NouriBashayer Nouri
2018
asked Jan 2 at 17:41
Bashayer NouriBashayer Nouri
2018
edited Jan 2 at 18:08
Bashayer Nouri
asked Jan 2 at 17:41
Bashayer NouriBashayer Nouri
2018
asked Jan 2 at 17:41
Bashayer NouriBashayer Nouri
2018
asked Jan 2 at 17:41
Bashayer NouriBashayer Nouri
2018
2018
1
$begingroup$
They have not multiplied by $ln$, they have taken the natural log of both the sides
$endgroup$
– Shubham Johri
Jan 2 at 17:45
$begingroup$
ohh okkk, thank you so much, I appreciate your comment a lot.
$endgroup$
– Bashayer Nouri
Jan 2 at 17:54
add a comment |
1
$begingroup$
They have not multiplied by $ln$, they have taken the natural log of both the sides
$endgroup$
– Shubham Johri
Jan 2 at 17:45
$begingroup$
ohh okkk, thank you so much, I appreciate your comment a lot.
$endgroup$
– Bashayer Nouri
Jan 2 at 17:54
1
1
$begingroup$
They have not multiplied by $ln$, they have taken the natural log of both the sides
$endgroup$
– Shubham Johri
Jan 2 at 17:45
$begingroup$
They have not multiplied by $ln$, they have taken the natural log of both the sides
$endgroup$
– Shubham Johri
Jan 2 at 17:45
$begingroup$
ohh okkk, thank you so much, I appreciate your comment a lot.
$endgroup$
– Bashayer Nouri
Jan 2 at 17:54
$begingroup$
ohh okkk, thank you so much, I appreciate your comment a lot.
$endgroup$
– Bashayer Nouri
Jan 2 at 17:54
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
You don’t “multiply” logs to both sides, as that simply makes no sense. You apply them to both sides, or you “take the log of both sides.”
$$8 = 7.1e^{10k}$$
$$frac{8}{7.1} = e^{10k}$$
Here, you apply the definition of the natural log:
$$e^a = b iff ln b = a$$
which yields
$$frac{8}{7.1} = e^{10k} iff 10k = lnleft(frac{8}{7.1}right)$$
$$k = frac{lnleft(frac{8}{7.1}right)}{10}$$
answered Jan 2 at 17:48
KM101KM101
5,9511523
$endgroup$
1
$begingroup$
Thank you so soooo much I needed this, have a nice day <3
$endgroup$
– Bashayer Nouri
Jan 2 at 17:55
2
$begingroup$
Glad I could help!
$endgroup$
– KM101
Jan 2 at 18:01
add a comment |
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1 Answer
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$begingroup$
You don’t “multiply” logs to both sides, as that simply makes no sense. You apply them to both sides, or you “take the log of both sides.”
$$8 = 7.1e^{10k}$$
$$frac{8}{7.1} = e^{10k}$$
Here, you apply the definition of the natural log:
$$e^a = b iff ln b = a$$
which yields
$$frac{8}{7.1} = e^{10k} iff 10k = lnleft(frac{8}{7.1}right)$$
$$k = frac{lnleft(frac{8}{7.1}right)}{10}$$
answered Jan 2 at 17:48
KM101KM101
5,9511523
$endgroup$
1
$begingroup$
Thank you so soooo much I needed this, have a nice day <3
$endgroup$
– Bashayer Nouri
Jan 2 at 17:55
2
$begingroup$
Glad I could help!
$endgroup$
– KM101
Jan 2 at 18:01
add a comment |
$begingroup$
You don’t “multiply” logs to both sides, as that simply makes no sense. You apply them to both sides, or you “take the log of both sides.”
$$8 = 7.1e^{10k}$$
$$frac{8}{7.1} = e^{10k}$$
Here, you apply the definition of the natural log:
$$e^a = b iff ln b = a$$
which yields
$$frac{8}{7.1} = e^{10k} iff 10k = lnleft(frac{8}{7.1}right)$$
$$k = frac{lnleft(frac{8}{7.1}right)}{10}$$
answered Jan 2 at 17:48
KM101KM101
5,9511523
$endgroup$
1
$begingroup$
Thank you so soooo much I needed this, have a nice day <3
$endgroup$
– Bashayer Nouri
Jan 2 at 17:55
2
$begingroup$
Glad I could help!
$endgroup$
– KM101
Jan 2 at 18:01
add a comment |
$begingroup$
You don’t “multiply” logs to both sides, as that simply makes no sense. You apply them to both sides, or you “take the log of both sides.”
$$8 = 7.1e^{10k}$$
$$frac{8}{7.1} = e^{10k}$$
Here, you apply the definition of the natural log:
$$e^a = b iff ln b = a$$
which yields
$$frac{8}{7.1} = e^{10k} iff 10k = lnleft(frac{8}{7.1}right)$$
$$k = frac{lnleft(frac{8}{7.1}right)}{10}$$
answered Jan 2 at 17:48
KM101KM101
5,9511523
$endgroup$
You don’t “multiply” logs to both sides, as that simply makes no sense. You apply them to both sides, or you “take the log of both sides.”
$$8 = 7.1e^{10k}$$
$$frac{8}{7.1} = e^{10k}$$
Here, you apply the definition of the natural log:
$$e^a = b iff ln b = a$$
which yields
$$frac{8}{7.1} = e^{10k} iff 10k = lnleft(frac{8}{7.1}right)$$
$$k = frac{lnleft(frac{8}{7.1}right)}{10}$$
answered Jan 2 at 17:48
KM101KM101
5,9511523
answered Jan 2 at 17:48
KM101KM101
5,9511523
answered Jan 2 at 17:48
KM101KM101
5,9511523
answered Jan 2 at 17:48
KM101KM101
5,9511523
5,9511523
1
$begingroup$
Thank you so soooo much I needed this, have a nice day <3
$endgroup$
– Bashayer Nouri
Jan 2 at 17:55
2
$begingroup$
Glad I could help!
$endgroup$
– KM101
Jan 2 at 18:01
add a comment |
1
$begingroup$
Thank you so soooo much I needed this, have a nice day <3
$endgroup$
– Bashayer Nouri
Jan 2 at 17:55
2
$begingroup$
Glad I could help!
$endgroup$
– KM101
Jan 2 at 18:01
1
1
$begingroup$
Thank you so soooo much I needed this, have a nice day <3
$endgroup$
– Bashayer Nouri
Jan 2 at 17:55
$begingroup$
Thank you so soooo much I needed this, have a nice day <3
$endgroup$
– Bashayer Nouri
Jan 2 at 17:55
2
2
$begingroup$
Glad I could help!
$endgroup$
– KM101
Jan 2 at 18:01
$begingroup$
Glad I could help!
$endgroup$
– KM101
Jan 2 at 18:01
add a comment |
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1
$begingroup$
They have not multiplied by $ln$, they have taken the natural log of both the sides
$endgroup$
– Shubham Johri
Jan 2 at 17:45
$begingroup$
ohh okkk, thank you so much, I appreciate your comment a lot.
$endgroup$
– Bashayer Nouri
Jan 2 at 17:54