Question

Write the equation in exponential form. Log 4 1/16 =-2

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the rule of logarithms

• $log_{b}$ x = n ⇔ x = $b^{n}$

Hence

with b = 4 and n = - 2

$log_{4}$ $\frac{1}{16}$ = - 2, then

$\frac{1}{16}$ = $4^{-2}$ ← in exponential form

Answer 2

ANSWER

The exponential form is

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

EXPLANATION

The given logarithm is

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

We want to write the given logarithm in exponential form:

We take the antilogarithm of both sides to obtain:

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

We simplify the left hand side to obtain:

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

Hence the exponential form is

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