We have been asked to Write the given equation in logarithmic form
The given equation is
[tex] 625=5^4 [/tex]
As we know the logarithmic and exponential functions are inverse of each other.
Also as we know from the property of the logarithm that
[tex] {Log_{a}}^{a}=1\\ [/tex]
Take Logarithm of base 5 on both the sides we get
[tex] {Log_{5}}^{625}={Log_{5}}^{5^4} [/tex]
Now using the Power property [tex] Loga^b=bloga [/tex], along with the above mentioned property we can write the above equation as below
[tex] {Log_{5}}^{625}=4*{Log_{5}}^{5}=4*1=4 [/tex]
Hence the Logarithmic Form of the given equation is
[tex] {Log_{5}}^{625}=4 [/tex]
