Answer:
[tex]log_5125=3[/tex]
Step-by-step explanation:
Given : [tex]log_5125[/tex]
We have to find the value of [tex]log_5125[/tex]
Consider the given expression [tex]log_5125[/tex]
Rewrite 125 in power- base form, [tex]125=5^3[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]
[tex]\log _5\left(5^3\right)=3\log _5\left(5\right)[/tex]
[tex]=3\log _5\left(5\right)[/tex]
[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1[/tex]
[tex]\log _5\left(5\right)=1[/tex]
[tex]3\log _5\left(5\right)=3[/tex]
Thus, [tex]log_5125=3[/tex]
