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#