How do you rewrite 10^u = v in logarithmic form?

1 Answer
Jun 9, 2017

log_10v=u

Explanation:

Take the base 10 logarithm of both sides

log_10(10^u)=log_10(v)

Using properties logarithms we can rewrite the left hand side.

u(log_10(10))=log_10(v)

u(1)=log_10(v)

log_10(v)=u

Remember that the logarithmic function is the inverse of the exponential function. So when you see

10^u=v the logarithm is asking what number do i have to raise the base to to get the argument of the logarithmic function.... for example log_10(100)=2 which is the inverse of
10^2=100