Question

solve: $\log_{4}(7t + 2) = 2$
$t = \square$
done

Explanation:

Step1: Convert log to exponential form

Using the definition of logarithms, if $\log_b(a) = c$, then $b^c = a$. Here, $b = 4$, $a = 7t + 2$, and $c = 2$. So we get $4^2 = 7t + 2$.

Step2: Simplify the exponential term

Calculate $4^2$, which is $16$. So the equation becomes $16 = 7t + 2$.

Step3: Solve for t

Subtract 2 from both sides: $16 - 2 = 7t$, which simplifies to $14 = 7t$. Then divide both sides by 7: $t = \frac{14}{7} = 2$.

Answer:

2