Solve for x:
(2 log(x))/log(10) + 2 = log(900)/log(10)
Rewrite the left hand side by combining fractions. (2 log(x))/log(10) + 2 = (2 (log(x) + log(10)))/log(10):
(2 (log(x) + log(10)))/log(10) = log(900)/log(10)
Divide both sides by 2/log(10):
log(x) + log(10) = log(900)/2
Subtract log(10) from both sides:
log(x) = log(900)/2 - log(10)
-log(10) + log(900)/2 = log(1/10) + log(sqrt(900)) = log(1/10) + log(30) = log(30/10) = log(3):
log(x) = log(3)
Cancel logarithms by taking exp of both sides:
x = 3