Mixing
Difference between the slope of a straight line in a linear plot, a log-log plot and a log-linear plot?
$begingroup$
This question is in the context of this statement:
On a logarithmic scale, a variable that increases at $5$% per
year will move along an upward-sloping line with a slope
of $0.05$
How do I interpret the slope of a line that's on a logarithmic scale? For example, on a linear scale, a slope of $0.05$ means that the $ y $ variable increases by $0.05$ with an unit increase in $ x $. What does a slope of $0.05$ mean on a semi-log plot (say, with the $ x $ - axis linear and $ y $ - axis logarithmic) or a log-log plot?
logarithms graphing-functions
edited Feb 3 at 1:01
J. W. Tanner
4,6541420
asked Feb 1 at 7:38
WorldGovWorldGov
345211
$endgroup$
add a comment |
$begingroup$
This question is in the context of this statement:
On a logarithmic scale, a variable that increases at $5$% per
year will move along an upward-sloping line with a slope
of $0.05$
How do I interpret the slope of a line that's on a logarithmic scale? For example, on a linear scale, a slope of $0.05$ means that the $ y $ variable increases by $0.05$ with an unit increase in $ x $. What does a slope of $0.05$ mean on a semi-log plot (say, with the $ x $ - axis linear and $ y $ - axis logarithmic) or a log-log plot?
logarithms graphing-functions
edited Feb 3 at 1:01
J. W. Tanner
4,6541420
asked Feb 1 at 7:38
WorldGovWorldGov
345211
$endgroup$
$begingroup$
I think in this case, the $y$-value is what has the logarithmic scale. So it means that instead of graphing $y=f(x)$, we plot $y' = log{y} = log{f(x)}$. If we say that this is linear, it means that $$ log{f(x)} = ax + b = 0.05x + b $$ and here $a=0.05$. So in reality, the true function looks something like $$ f(x) = e^{0.05 x +b} $$
$endgroup$
– Matti P.
Feb 1 at 7:49
add a comment |
$begingroup$
This question is in the context of this statement:
On a logarithmic scale, a variable that increases at $5$% per
year will move along an upward-sloping line with a slope
of $0.05$
How do I interpret the slope of a line that's on a logarithmic scale? For example, on a linear scale, a slope of $0.05$ means that the $ y $ variable increases by $0.05$ with an unit increase in $ x $. What does a slope of $0.05$ mean on a semi-log plot (say, with the $ x $ - axis linear and $ y $ - axis logarithmic) or a log-log plot?
logarithms graphing-functions
edited Feb 3 at 1:01
J. W. Tanner
4,6541420
asked Feb 1 at 7:38
WorldGovWorldGov
345211
$endgroup$
This question is in the context of this statement:
On a logarithmic scale, a variable that increases at $5$% per
year will move along an upward-sloping line with a slope
of $0.05$
How do I interpret the slope of a line that's on a logarithmic scale? For example, on a linear scale, a slope of $0.05$ means that the $ y $ variable increases by $0.05$ with an unit increase in $ x $. What does a slope of $0.05$ mean on a semi-log plot (say, with the $ x $ - axis linear and $ y $ - axis logarithmic) or a log-log plot?
logarithms graphing-functions
logarithms graphing-functions
edited Feb 3 at 1:01
J. W. Tanner
4,6541420
asked Feb 1 at 7:38
WorldGovWorldGov
345211
edited Feb 3 at 1:01
J. W. Tanner
4,6541420
asked Feb 1 at 7:38
WorldGovWorldGov
345211
edited Feb 3 at 1:01
J. W. Tanner
4,6541420
edited Feb 3 at 1:01
J. W. Tanner
4,6541420
edited Feb 3 at 1:01
J. W. Tanner
4,6541420
4,6541420
asked Feb 1 at 7:38
WorldGovWorldGov
345211
asked Feb 1 at 7:38
WorldGovWorldGov
345211
asked Feb 1 at 7:38
WorldGovWorldGov
345211
345211
$begingroup$
I think in this case, the $y$-value is what has the logarithmic scale. So it means that instead of graphing $y=f(x)$, we plot $y' = log{y} = log{f(x)}$. If we say that this is linear, it means that $$ log{f(x)} = ax + b = 0.05x + b $$ and here $a=0.05$. So in reality, the true function looks something like $$ f(x) = e^{0.05 x +b} $$
$endgroup$
– Matti P.
Feb 1 at 7:49
add a comment |
$begingroup$
I think in this case, the $y$-value is what has the logarithmic scale. So it means that instead of graphing $y=f(x)$, we plot $y' = log{y} = log{f(x)}$. If we say that this is linear, it means that $$ log{f(x)} = ax + b = 0.05x + b $$ and here $a=0.05$. So in reality, the true function looks something like $$ f(x) = e^{0.05 x +b} $$
$endgroup$
– Matti P.
Feb 1 at 7:49
$begingroup$
I think in this case, the $y$-value is what has the logarithmic scale. So it means that instead of graphing $y=f(x)$, we plot $y' = log{y} = log{f(x)}$. If we say that this is linear, it means that $$ log{f(x)} = ax + b = 0.05x + b $$ and here $a=0.05$. So in reality, the true function looks something like $$ f(x) = e^{0.05 x +b} $$
$endgroup$
– Matti P.
Feb 1 at 7:49
$begingroup$
I think in this case, the $y$-value is what has the logarithmic scale. So it means that instead of graphing $y=f(x)$, we plot $y' = log{y} = log{f(x)}$. If we say that this is linear, it means that $$ log{f(x)} = ax + b = 0.05x + b $$ and here $a=0.05$. So in reality, the true function looks something like $$ f(x) = e^{0.05 x +b} $$
$endgroup$
– Matti P.
Feb 1 at 7:49
add a comment |
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$begingroup$
I think in this case, the $y$-value is what has the logarithmic scale. So it means that instead of graphing $y=f(x)$, we plot $y' = log{y} = log{f(x)}$. If we say that this is linear, it means that $$ log{f(x)} = ax + b = 0.05x + b $$ and here $a=0.05$. So in reality, the true function looks something like $$ f(x) = e^{0.05 x +b} $$
$endgroup$
– Matti P.
Feb 1 at 7:49