Solve for $x : 5 ^ { - x / 2 } = 0.0052$. Round to 3 decimal places.
A) $6.535$
B) $10.518$
C) $13.737$
D) $- 13.737$
E) $- 3.268$

Question

Quizplus · Accepted Answer

To solve $5^{-x/2} = 0.0052$, first express 0.0052 in terms of a power of 5. Since $5^{-3} = 0.008$, 0.0052 is not a perfect power of 5, but we can use logarithms to solve for $x$. Convert the equation to logarithmic form: $-\frac{x}{2} = \log_5(0.0052)$. Then, use the change of base formula to convert to a common logarithm or natural logarithm: $-\frac{x}{2} = \frac{\log(0.0052)}{\log(5)}$. Solving for $x$ gives $x \approx 6.535$, rounding to three decimal places.

Solve For x:5−x/2=0.0052x : 5 ^ { - x / 2 } = 0.0052x:5−x/2=0.0052

Solve For $x : 5 ^ { - x / 2 } = 0.0052$