Question

30 change the logarithmic equation \\( \log_{3} a = -8 \\) to an equivalent equation involving an exponent. what is an equivalent equation involving an exponent?

Explanation:

Step1: Recall the logarithmic to exponential conversion formula

The definition of a logarithm states that if $\log_{b}x = y$, then the equivalent exponential form is $b^{y}=x$.

Step2: Apply the formula to the given logarithmic equation

In the given equation $\log_{3}a=-8$, we have $b = 3$, $x = a$, and $y=-8$. Substituting these values into the exponential form formula $b^{y}=x$, we get $3^{-8}=a$.

Answer:

$3^{-8}=a$