Question

What is the solution of the following equation?

Answer 1

\[2^{2x} = 8^{x + 1}\]

Answer 2

re-write 8 as \(2^3\)

Answer 3

So then it would be \[2^{2x} = 2^{3x + 1}\] , or...?

Answer 4

almost.

use the idea
\[ \left(a^b\right)^c = a^{bc}\]
multiply the exponents.

in your case
\[ 2^{2x} = (2^3)^{(x + 1)} \]

Answer 5

notice that 3*(x+1) is not 3x+1

Answer 6

you distribute the 3: 3*x + 3*1

Answer 7

Ohh okay! I see what I did wrong

Answer 8

\[ 2^{2x} = 2^{3x + 3} \]

common sense should tell you that 2 to some power 2x is the same as 2 to some power 3x+3 means the exponents must be the same number:

2x must equal 3x+3
2x = 3x+3

solve for x

Answer 9

Okay! I can take it from here (: Again, thank you so much!