Indices Question.

**ns2583** · January 13th 2009, 06:22 AM

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

The equation is

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

Thanks in advance.

**Danny** · January 13th 2009, 06:25 AM

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

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

Thanks in advance.

Note that

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

**ns2583** · January 13th 2009, 06:28 AM

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.

**Danny** · January 13th 2009, 06:39 AM

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.

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