Two Four Eight

Algebra Level 1

8 x + 2 = 4 x + 4 , x = ? \Large 8^{x+2} = 4^{x+4} \quad,\quad x = \ ?


The answer is 2.

Gulamo Jamal by Gulamo Jamal , 35, Mozambique

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

3 solutions

Ashish Menon
May 29, 2016

8 x + 2 = 4 x + 4 2 3 x + 6 = 2 2 x + 8 3 x + 6 = 2 x + 8 x = 2 \begin{aligned} 8^{x + 2} & = 4^{x + 4}\\ 2^{3x + 6} & = 2^{2x + 8}\\ 3x + 6 & = 2x + 8\\ x & = \color{#69047E}{\boxed{2}} \end{aligned}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Taking log ⁡ 2 \log_{2} on both sides we get, ( x + 2 ) log ⁡ 2 8 = ( x + 4 ) log ⁡ 2 4 ⇒ 3 ( x + 2 ) = 2 ( x + 4 ) ⇒ x = 2 (x+2)\log_{2}8 = (x+4)\log_{2}4 \Rightarrow 3(x+2) =2(x+4) \Rightarrow x=\boxed{2}

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Gulamo Jamal
Jun 27, 2015

〖〖(2〗^3)〗^(x+2)=〖〖(2〗^2)〗^(x+4) 3x+6=2x+8 x=2

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...