2 Answers

The Rat · Answer 1 · 2022-10-28T18:45:10+0000

Answer:

The base is:
$3 \sqrt[3]{4}$

Explanation:

Given

$f(x) = (1)/(4)(\sqrt[3]{108})^x$

Required

The base

Expand 108

$f(x) = (1)/(4)(\sqrt[3]{3^3 * 4})^x$

Rewrite the exponent as:

f(x) = (1)/(4)(3^3 * 4)^(1)/(3)^x

Expand

f(x) = (1)/(4)(3^3^(1)/(3) * 4^(1)/(3))^x

f(x) = (1)/(4)(3 * 4^(1)/(3))^x

Rewrite as:

$f(x) = (1)/(4)(3 \sqrt[3]{4})^x$

An exponential function has the following form:

y=ab^x

Where

$b \to base$

By comparison:

$b =3 \sqrt[3]{4}$

So, the base is:
$3 \sqrt[3]{4}$

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