Question

Which of the following is the inverse of y=12^x ?

a. y= log 1\12x
b. y= log12 1/x
c. y= logx 12
d. y= log12x

Answer 1

ANSWER

$y = log_{12}(x)$

EXPLANATION

We want to find the inverse of the exponential function,

$y = {12}^{x}$

The above function is an exponential function, so we expect the inverse to be a logarithmic function.

We now interchange x and y.

$x = {12}^{y}$

We now make y the subject by taking antilogarithm of both sides to obtain,

$y = log_{12}(x)$

This last function is the inverse of

.
$y = 12^x$

Hence the correct answer is D

Answer 2

The inverse of the function $\rm log_{12}y = x$ is $y= log_{12} \dfrac{1}{x}$.

Given to us

$y = 12^x$

The inverse of a function y which is dependent on x, we solve the function such that the function becomes independent of x and depends on y.

What is the inverse of the function $\rm log_{12}y = x$?

We know that to write the inverse of a function y which is dependent on x, we solve the function such that the function becomes independent of x and depends on y.

$y = 12^x$

Taking antilog,

$\rm log_{12}y = x$

Substitute the values,

$y= log_{12} \dfrac{1}{x}$

Hence, the inverse of the function is $y= log_{12} \dfrac{1}{x}$.

Learn more about the Inverse function:

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