Question

solve for x.
3 log₄(-2x) = 6
x =

Explanation:

Step1: Divide both sides by 3

To isolate the logarithmic term, we divide both sides of the equation \( 3\log_{4}(-2x) = 6 \) by 3.
\( \frac{3\log_{4}(-2x)}{3} = \frac{6}{3} \)
Simplifying, we get \( \log_{4}(-2x) = 2 \).

Step2: Convert to exponential form

Recall that if \( \log_{b}(a) = c \), then \( b^{c} = a \). Using this property, we convert \( \log_{4}(-2x) = 2 \) to exponential form.
\( 4^{2} = -2x \)

Step3: Simplify and solve for x

Calculate \( 4^{2} \), which is 16. So the equation becomes \( 16 = -2x \).
To solve for \( x \), divide both sides by -2:
\( x = \frac{16}{-2} = -8 \).

Answer:

\( x = -8 \)