Question

if \\(\log_{4}(-2x + 8) = 3\\), then what is the value of \\(x\\)?

a.) -28
b.) 2
c.) 36
d.) -12

Explanation:

Convert the logarithmic equation to exponential form

Using the Logarithm Definition knowledge point

$$
LATEXBLOCK0
$$

Evaluate the exponent

Using the Exponentiation Rules knowledge point

$$ 4^3 = 64 $$

Solve the linear equation for x

Using the Linear Equations knowledge point

$$
LATEXBLOCK1
$$

Verify the solution

Using the Logarithm Definition knowledge point

$$
LATEXBLOCK2
$$

Answer:

• a.) -28 (Correct answer)
• b.) 2
• c.) 36
• d.) -12