Indices

Algebra Level 1

4 x + 2 = 2 3 x + 1 , x = ? \large 4^{x+2} = 2^{3x+1} \quad,\quad x = \, ?

5 3 4.5 4

Akwesi Barnes by akwesi barnes , 22, Ghana

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2 solutions

4 x + 2 = 2 3 x + 1 ( 2 2 ) x + 2 = 2 3 x + 1 2 2 x + 4 = 2 3 x + 1 ⟹ 2 x + 4 = 3 x + 1 4 − 1 = 3 x − 2 x x = 3 \begin{aligned} 4^{x+2}&=2^{3x+1}\\ (2^2)^{x+2}&=2^{3x+1}\\ 2^{2x+4}&=2^{3x+1}\\ \implies 2x+4&=3x+1\\ 4-1&=3x-2x\\ x&=3 \end{aligned}

2 Helpful 1 Interesting 0 Brilliant 0 Confused
Akwesi Barnes
Jan 11, 2016

4^x+2=2^3x+1. =2^2(x+2)=2^3x+1. equating the indices, we get 2(X+2)=3X+1. then 2x+4=3x+1. therefore x= 3

3 Helpful 0 Interesting 0 Brilliant 1 Confused

Problem with this is that it could have really used latex markdown or be better clarified using parenthesis to start with. The way it appears, the problem solver is supposed to add 2 to 4^x and on the other side add 1 to 2^3x. But by the looks of your solution what you really meant is...

4^(x+2)=2^(3x+1)

...or...

4 x + 2 = 2 3 x + 1 4^{x+2}=2^{3x+1}

😕?

Jeff Carter - 5 years, 5 months ago

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