Question

Find log\(_{5}\)(125) + log\(_{2}\)(1/16)

• A. 0
• B. 1
• C. 2
• D. -1

Hint:

Express $125$ as a power of $5$ and $1/16$ as a power of $2$. The reciprocal in the second term requires a negative exponent.

Answer 1

The Correct Option is D

Concept:

• Use the defining equation $\log_b x=y$ if $b^y=x$.
• Solve the two exponent equations before adding.

Step 1: Let $5^x=125$.
Because $5^3=125$, $x=3$.

Step 2: Let $2^y=1/16$.
Because $2^{-4}=1/16$, $y=-4$.

Step 3: Combine the exponents.
$x+y=3-4=-1$.

Final Answer: $-1$