# Variable in Exponents

1. Jan 14, 2009

### Mentallic

1. The problem statement, all variables and given/known data
Solve for x
$$5^{3x}-12^x+2^{\frac{x}{2}}=5$$

2. Relevant equations
logarithm rules?
log(a+b)=?

3. The attempt at a solution
Taking the logarithm of both sides only makes things worse from what I can see.
So really, I don't know how to start.
$$x\approx 0.386744$$

2. Jan 14, 2009

### tiny-tim

hmm … that's 125x - 12x + (√2)x = 5 …

i can't see any way of solving that except by numerical approximation

3. Jan 14, 2009

### Mentallic

Is this possibly due to the lack of understanding with this maths or because it cannot be solved with an exact answer? Such as 'exact' answers with a series of logarithms, even though the logs themselves are approximated.
Any idea how I could go about obtaining a reasonably accurate numerical approximation?