1. ## Indices Question.

Aight, so the question is to "Solve the following equation".
Unfortunately, I have no clue where to start...

The equation is

$2^x + 2^{2x+3} =72$

2. Originally Posted by ns2583
Aight, so the question is to "Solve the following equation".
Unfortunately, I have no clue where to start...

The equation is

$2^x + 2^{2x+3} =72$

Note that

$2^{2x+3} = 2^3 \cdot 2^{2x} = 8 \cdot \left( 2^{x} \right)^2.$

3. Originally Posted by danny arrigo
Note that

$2^{2x+3} = 2^3 \cdot 2^{2x} = 8 \cdot \left( 2^{x} \right)^2.$
I still don't know what goes next?
Sorry.

4. Originally Posted by ns2583
I still don't know what goes next?
Sorry.
So

$2^x + 8 \cdot \left( 2^{x} \right)^2 = 72,$

If we let $y = 2^x$ we get a quadratic equation for y.