Question

Express 125 = 5x as a logarithmic equation.

Answer 1

Answer: x log[5] = log[125]

Explanation:

The original expression is 125 = 5^x

To express that as a logarithmic equation take logarithms on both sides:

log [125] = [log 5^x]

By the properties of the logartims of powers that is:

log [125] = x log[5]

And that is the equation required.

If you want to solve it, you can do 125 = 5^2, and apply the same property (logarithm of a power) to the left side, yielding to:

log [5^2 ]= x log[5]

=> 2 log[5] = x log[5]

=> 2 = x