Answer:
[tex](\frac{4}{3})=log_{125}(625)[/tex]
Step-by-step explanation:
The given equation is:
[tex]125^{\frac{4}{3}}=625[/tex]
Now, taking log to base 125 on both sides, we get
[tex]log_{125}(125^{\frac{4}{3}})=log_{125}(625)[/tex]
[tex](\frac{4}{3})log_{125}(125)=log_{125}(625)[/tex]
Now, log to the base 125 of 125 is equal to one as log to the base a of a is equal to one, therefore,
[tex](\frac{4}{3})=log_{125}(625)[/tex]
which is the required logarithmic form.
