2016 AMC 10A Problem 2

Problem 2 of 25EasierAlgebra

For what value of

x

does

10^{x} \cdot 100^{2x}=1000^{5}?

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Solution

Rewrite all bases as powers of

10

\small 10^x\cdot100^{2x}=10^x\cdot(10^2)^{2x}=10^{5x},

and

1000^5=(10^3)^5=10^{15}.

Therefore

5x=15

, so

x=3

. Thus, the correct answer is C.

Concepts: exponent

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.