consider the equation log(3x - 1) = log₂8. explain why 3x - 1 is not equal to 8. describe the steps you…

Explanation:

Step1: Recall log - base relationship

The left - hand side is $\log(3x - 1)$ (assuming base 10) and the right - hand side is $\log_28$. Since the bases of the logarithms are different (10 and 2), we can't directly set $3x - 1$ equal to 8.

Step2: Evaluate $\log_28$

We know that $2^3=8$, so $\log_28 = 3$. The equation becomes $\log(3x - 1)=3$.

Step3: Rewrite in exponential form

By the definition of logarithms, if $\log_{a}b=c$, then $b = a^c$. Here $a = 10$, $c = 3$, so $3x-1=10^3$.

Answer:

$3x - 1$ is equal to 1000.