Question

solve the equation. log₄(x + 6)=2 select the correct choice below and fill in any answer boxes present in your choice. a. x = (simplify your answer, including any radicals. use integers or fractions for any numbers in the expression. use a comma) b. there is no solution.

Explanation:

Step1: Convert to exponential form

By the definition of logarithms, if $\log_{a}b = c$, then $b=a^{c}$. So for $\log_{4}(x + 6)=2$, we have $x + 6=4^{2}$.

Step2: Calculate the value of $4^{2}$

$4^{2}=16$, so the equation becomes $x + 6=16$.

Step3: Solve for $x$

Subtract 6 from both sides of the equation: $x=16 - 6$.
$x = 10$

Answer:

A. $x = 10$