Solving Log Equations: 2^x * 4^(x+5) = 4^(2x-1)

[Corkery]

Homework Statement

Solve the equation:
2^x multiplied by 4^(x + 5) = 4^(2x - 1)

Homework Equations

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.

 

[danago]

When you have $$2^x2^{2x+10}$$, you don't multiply the indexes, you add them.

 

[HallsofIvy]

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!