Is $R(x)=4 ln(x)$ an exponential function?

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Answer 1 · 2018-06-26T12:26:45

$color(blue)("No, it's a logarithmic function")$

$R(x)=4ln(x)$ is a logarithmic function.

Logarithmic functions are the inverses of exponential functions.

If we rearrange $y=4ln(x)$ to find $x$ as a function of $y$

$y=4ln(x)$

$y/4=ln(x)$

$e^(y/4)=e^(ln(x))$

$e^(y/4)=x$

Substituting $x=y$

$y=e^(x/4)color(white)(88)$ This is an exponential function.

So:

$y=e^(x/4)$ is the inverse of the logarithmic function $y=4ln(x)$

Conversely: $y=4ln(x)$ is the inverse of the exponential function $y=e^(x/4)$

Is R(x)=4 ln(x)R(x)=4 ln(x) an exponential function?