Question

solve the equation. log₂(x - 6)=5 select the correct choice below and fill in any answer b. a. x = (simplify your answer, including any radicals. us 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 $\log_{2}(x - 6)=5$, we have $x-6 = 2^{5}$.

Step2: Calculate $2^{5}$

$2^{5}=2\times2\times2\times2\times2=32$. So the equation becomes $x - 6=32$.

Step3: Solve for $x$

Add 6 to both sides of the equation: $x=32 + 6$.
$x=38$

Answer:

A. $x = 38$