I read your equation as: 1/2* log(5x) + log(5) = 1
Solve for x:
log(5) + 1/2 log(5 x) = 1
Rewrite the left hand side by combining fractions. log(5) + 1/2 log(5 x) = 1/2 (2 log(5) + log(5 x)):
1/2 (2 log(5) + log(5 x)) = 1
Multiply both sides by 2:
2 log(5) + log(5 x) = 2
Subtract 2 log(5) from both sides:
log(5 x) = 2 - 2 log(5)
2 - 2 log(5) = 2 + log(1/5^2) = 2 + log(1/25):
log(5 x) = 2 + log(1/25)
Cancel logarithms by taking exp of both sides:
5 x = e^(2 + log(1/25))
e^(2 + log(1/25)) = e^(log(1/25)) e^2 = e^2/25:
5 x = (e^2)/(25)
Divide both sides by 5:
Answer: | x = e^2/125
