Question

question 13 of 15, step 1 of 1
solve the following logarithmic equation, using a calculator if necessary to evaluate the logarithm. write your answer as a fraction or round your answer to two decimal places.
\\(\log_{4}(2x - 8) = 2\\)
answer
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\\(x = \\)

Explanation:

Step1: Convert log to exponential

Using the definition of logarithms, if $\log_b(a) = c$, then $b^c = a$. So for $\log_4(2x - 8) = 2$, we get $4^2 = 2x - 8$.

Step2: Simplify the equation

Calculate $4^2 = 16$, so the equation becomes $16 = 2x - 8$.

Step3: Solve for x

Add 8 to both sides: $16 + 8 = 2x$, which simplifies to $24 = 2x$. Then divide both sides by 2: $x = \frac{24}{2} = 12$.

Answer:

$x = 12$