Solve the equation. Give an approximate solution to four decimal places.
-$$4 ^ { x } = 11$$
A) $\{ 0.3636 \}$
B) $\{ 1.7297 \}$
C) $\{ 3.3242 \}$
D) $\{ 0.5781 \}$

Question

Quizplus · Accepted Answer

To solve the equation $4^x = 11$, we take the logarithm of both sides. Using the logarithm base 10 or natural logarithm (ln) is common. Here, we'll use the natural logarithm for simplicity: $\ln(4^x) = \ln(11)$. By the property of logarithms, this becomes $x \ln(4) = \ln(11)$. Solving for $x$ gives $x = \frac{\ln(11)}{\ln(4)}$. Using a calculator, this approximately equals $1.7297$.

Solve the Equation 4x=114 ^ { x } = 114x=11 A) {0.3636}\{ 0.3636 \}{0.3636}

Solve the Equation $4 ^ { x } = 11$ A) $\{ 0.3636 \}$