#1**+1 **

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**

Guest May 1, 2017