Respuesta :

Answer:

see explanation

Step-by-step explanation:

Using the rule of logarithms

• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Hence

with b = 4 and n = - 2

[tex]log_{4}[/tex] [tex]\frac{1}{16}[/tex] = - 2, then

[tex]\frac{1}{16}[/tex] = [tex]4^{-2}[/tex] ← in exponential form

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ANSWER

The exponential form is

[tex] \frac{1}{16} = {4}^{ - 2} [/tex]

EXPLANATION

The given logarithm is

[tex] log_{4}( \frac{1}{16} ) = - 2[/tex]

We want to write the given logarithm in exponential form:

We take the antilogarithm of both sides to obtain:

[tex] {4}^{log_{4}( \frac{1}{16} )} = {4}^{ - 2} [/tex]

We simplify the left hand side to obtain:

[tex] \frac{1}{16} = {4}^{ - 2} [/tex]

Hence the exponential form is

[tex] \frac{1}{16} = {4}^{ - 2} [/tex]

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