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.
-$\left( \frac { 1 } { 2 } \right) ^ { x } = 15$
A) {-0.26}
B) {-7.50}
C) {3.91}
D) {-3.91}

Question

Quizplus · Accepted Answer

To solve the equation $\left( \frac { 1 } { 2 } \right) ^ { x } = 15$, we can take the logarithm of both sides. Using the property of logarithms, we get $x \log\left(\frac{1}{2}\right) = \log(15)$. Solving for $x$ gives $x = \frac{\log(15)}{\log\left(\frac{1}{2}\right)}$, which approximately equals -3.91.

Choose the One Alternative That Best Completes the Statement or Answers