Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 2.1 Junior Find the answer

What is the value of $n$ if $2^{n}=8^{20}$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Since $8=2 \times 2 \times 2=2^{3}$ , then $8^{20}=\left(2^{3}\right)^{20}=2^{3 \times 20}=2^{60}$ . Thus, if $2^{n}=8^{20}$ , then $n=60$ .

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