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Problem 200

Algebra Difficulty 1.4 Find the answer CEMC Fermat · Canada · 2021

If 3x=53^{x}=5, the value of 3x+23^{x+2} is

1010
2525
21872187
1414
4545

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

Using exponent laws, 3x+2=3x⋅32=3x⋅93^{x+2} = 3^x \cdot 3^2 = 3^x \cdot 9.

Since 3x=53^x=5, then 3x+2=3x⋅9=5⋅9=453^{x+2} = 3^x \cdot 9 = 5 \cdot 9 = 45.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.