QuestionRewrite $\left(\frac{1}{3}\right)^{-4}=81$ as a logarithmic equation.

Studdy Solution

STEP 1

Assumptions1. We are given the exponential equation $\left(\frac{1}{3}\right)^{-4}=81$ . . We need to rewrite this equation in logarithmic form.

STEP 2

The general form of a logarithmic equation is $\log_b a = c$ , where $b$ is the base, $a$ is the argument, and $c$ is the result. This is equivalent to the exponential equation $b^c = a$ .

STEP 3

We can rewrite the given exponential equation $\left(\frac{1}{3}\right)^{-}=81$ in logarithmic form by identifying the base, the exponent, and the result.

STEP 4

In the given exponential equation, the base is $\frac{1}{3}$ , the exponent is $-4$ , and the result is $81$ .

STEP 5

Substitute these values into the general form of a logarithmic equation to get the equivalent logarithmic equation.
$\log_{\frac{1}{3}}81 = -4$ This is the correct logarithmic form of the given exponential equation. The other options are incorrect because they do not correctly match the base, argument, and result of the given exponential equation.

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