# Log equations AGAIN!

1. Apr 23, 2007

### Corkery

1. The problem statement, all variables and given/known data
Solve the equation:
2^x multiplied by 4^(x + 5) = 4^(2x - 1)

2. Relevant equations

3. The attempt at a solution

2^x multiplied by 2^2(x+5)=2^2(2x-1)
x(2x+10)=4x-2
2x^2+10x=4x-2

and that's as far as i could get before I was completely stuck. But this could be completely wrong.

2. Apr 23, 2007

### danago

When you have $$2^x2^{2x+10}$$, you dont multiply the indexes, you add them.

3. Apr 24, 2007

### HallsofIvy

Staff Emeritus
As danago said, $$2^x2^{2x+10}= 2^{3x+10}= 2^{4x-2}$$. That gives a simple linear equation for x.

However, IF 2x^2+10x=4x-2 had been correct, that shouldn't give you any problem. It is a quadratic equation and, if you can't factor it, you can use the quadratic formula!

Last edited: Apr 25, 2007