For what value of x does 10^x× 100^2x=1000^5?

2016 AMC 12A Problem 2

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For what value of

x

does

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

1

2

3

4

5

Concepts:exponent

Write every base as a power of

10

The left side becomes

10^{5x}

and the right side

10^{15}

Since

100=10^2

and

1000=10^3,

the equation becomes

10^x\cdot 10^{4x}=10^{15},

10^{5x}=10^{15}.

Then

5x=15,

giving

x=3.

Thus, the correct answer is C.