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Algebra Level 1

Before we dive into Euler's formula and Complex Algebra, let's test your intuitive understanding of non-complex algebra.

9 a = 25 3 a = ? \begin{aligned} \large 9^a&\large= 25 \\ \\ \large 3^a &\large = \ ? \end{aligned}

What goes at the question mark in the equations above?

Hint: There's a much faster way than solving for a . a. You are not a robot, and you don't need a calculator to solve this!

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Queenbe Monyei by Queenbe Monyei , 36, USA

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1 solution

Discussions for this problem are now closed

Eli Ross Staff
Dec 21, 2016

In short: take the square root of both sides of the first equation:

9 a = 25 ( 3 2 ) a = 5 3 2 a = 5 ( 3 a ) 2 = 5 3 a = 5. \begin{aligned} \sqrt{9^a} &= \sqrt{25} \\ \sqrt{\left(3^2\right)^a} & = \ 5 \\ \sqrt{3^{2a}} & = \ 5 \\ \sqrt{\left(3^a\right)^2} & = \ 5 \\ 3^a & = \ 5. \end{aligned}

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