Choose the one alternative that best completes the statement or answers the question.
Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the
solution.
-$$4 ^ { 6 x } = 4.8$$
A) $\{ 0.19 \}$
B) $\{ 6.79 \}$
C) $\{ 0.22 \}$
D) $\{ 6.20 \}$

Question

Quizplus · Accepted Answer

To solve the equation $4^{6x} = 4.8$, we first take the logarithm of both sides. Using the base 10 logarithm for simplicity, we get $\log(4^{6x}) = \log(4.8)$. Applying the logarithm power rule, this becomes $6x \log(4) = \log(4.8)$. Solving for $x$ gives $x = \frac{\log(4.8)}{6\log(4)}$. Using a calculator to find this value gives $x \approx 0.19$, which matches choice A.

Choose the One Alternative That Best Completes the Statement or Answers