Solve Exponential Variable Equations with Logarithms

[Mentallic]

Homework Statement

Solve for x
$$5^{3x}-12^x+2^{\frac{x}{2}}=5$$

Homework Equations

logarithm rules?
log(a+b)=?

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.
$$x\approx 0.386744$$

 

[tiny-tim]

Solve for x
$$5^{3x}-12^x+2^{\frac{x}{2}}=5$$

hmm … that's 125^x - 12^x + (√2)^x = 5 …

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

 

[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?