Solve for $x$ without using logs: $3^{2x-1} = 9^{-x}$

Question

Any clues on how to start this problem would be welcomed.

score 6 · Answer 1 · edited Jul 30 '13 at 00:48

6

$$\begin{align}3^{2x-1}=9^{-x} &\implies3^{2x-1}=3^{2(-x)}\\ &\implies 2x-1=-2x\\ &\implies4x-1=0\\ &\implies4x=1\\ &\implies x=\dfrac{1}{4}\end{align}$$

The important thing is to recognize that $9=3^2$ and recall that if you have $a^x=a^y\implies x=y,$ for $x,y \in \mathbb{R}$.

edited Jul 30 '13 at 00:48

Cameron Buie

102,994

answered Jul 30 '13 at 00:41

Sujaan Kunalan

10,944

(+1) I've edited the layout of your answer. See what you think. (Love the profile pic, by the way.) – Cameron Buie Jul 30 '13 at 00:49
@CameronBuie: The layout you've provided is fine. (And thanks) :) – Sujaan Kunalan Jul 30 '13 at 01:06

score 1 · Answer 2 · answered Jul 30 '13 at 00:54

1

Make base the same and equate exponents HINT : $ 3^2 = 9 $ (so make both LHS nad RHS base as 3 )

answered Jul 30 '13 at 00:54

Harish Kayarohanam

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2
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Solve for $x$ without using logs: $3^{2x-1} = 9^{-x}$

2 Answers2