Answer :
Given:
The equation is
[tex]\log_3625=x[/tex]
To find:
The value of x.
Solution:
We have,
[tex]\log_3625=x[/tex]
It can be written as
[tex]\log_3(5)^4=x[/tex]
[tex]4\log_3(5)=x[/tex] [tex][\because \log x^n=n\log x][/tex]
[tex]4\dfrac{\log (5)}{\log (3)}=x[/tex] [tex][\because \log_ab=\dfrac{\log_xb}{\log_xa}][/tex]
[tex]4\times \dfrac{0.69897}{0.47712}=x[/tex]
[tex]x\approx 5.8599[/tex]
Therefore, the value of x is about 5.8599.