Question

Write the equation in exponential form. log4116 = −2

Answer 1

The answer is $4^{-2}=\frac {1}{16}$.

$log_4 \frac {1}{16}=-2$

The subscript for log is 4, which is the base of the exponent. What the log function is equal to is the exponent, which is -2. Finally the number next to the log is the answer and that is $\frac {1}{16}$

Answer 2

ANSWER

The exponential form is,

$\frac{1}{16} = {4}^{ - 2}$


EXPLANATION

The logarithmic expression given to us is

$log_{4}( \frac{1}{16} ) = - 2$


We want to rewrite this in the exponential form,

We take the antilogarithm of both sides to base 4.


This implies that,

${4}^{log_{4}( \frac{1}{16} )} = {4}^{ - 2}$


Recall that,

${q}^{log_{q}( p )} = p$


This implies that,

$\frac{1}{16} = {4}^{ - 2}$