The value of log_5((125)(625))/(25) is equal to:

1950 AMC 12 Problem 25

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25.

The value of

\log_5\dfrac{(125)(625)}{25}

is equal to:

725

6

3125

5

None of these answers

Write

125,

625,

and

25

as powers of

5

The logarithm’s argument simplifies to

5^{3+4-2}

Since

125=5^3,

625=5^4,

and

25=5^2,

\begin{aligned} &\log_5\frac{(125)(625)}{25}\\ &=\log_5\left(5^{3+4-2}\right)\\ &=\log_5(5^5)=5. \end{aligned}

Thus, the correct answer is D.