5^5x-2 = (5^x)^2
Since theres an exponent of an exponent, we can multiply the exponents together.
5^5x-2 = 5^2x
To get rid of the exponents, we can take the log of 5 so that the exponents become coefficients
log(5^5x-2) = log (5^2x)
(5x-2)( log(5) ) = (2x)( log(5) )
Next we can divide boths sides by log(5) to cancel them out so that we get:
5x-2 = 2x
Add 2 to both sides
5x = 2x + 2
Minus 2x on both sides
3x = 2
x = 2/3 or 0.667
