Exponents can be tricky

Algebra Level 3

When 3 x 5 2 3^x5^2 is divided by 3 5 5 3 3^5 5^3 ; the quotient terminates with one decimal digit.

Which of the given options must be true?

x < 5 x<5 x is odd x ≥ 5 x\ge 5 x = 5 x=5 x is even

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Hana Wehbi
Aug 2, 2017

Notice that if x < 5 x < 5 , the given fraction 3 x 5 2 3 5 5 3 = 3 x 3 5 × 5 = ( 0.2 ) ( 3 x 3 5 ) \large \frac{3^x5^2}{3^55^3} = \frac{3^x}{3^5\times 5}= (0.2)(\frac{3^x}{3^5}) will yield a repeating decimal. Look at 1 3 = 0.333 ⋯ ⟹ x ≥ 5 \frac{1}{3}=0.333\dots\implies x\ge 5 .

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