G'day, Lucy.
We can use a hat, ^, to denote an exponent.
So we have
2.5^(x+2) = 8
We need to take logs (of any base, so long as we are consistent with it) of both sides:
log[2.5^(x+2)] = log(8)
From the log rule log(x^n) = nlog(x), we have:
(x+2)log(2.5) = log(8)
We can now solve for x:
(x+2) = log(8)/log(2.5)
x = log(8)/log(2.5) - 2
