Answer:
[tex]log_{4}(125)=3.48289[/tex]
Step-by-step explanation:
Changing Bases to Evaluate Logarithms
[tex]log_{4}(125)[/tex]
Apply change of base formula'
[tex]log_b(a)= \frac{log a}{log b}[/tex]
log term should be the numerator and denominator is the log base
[tex]log_{4}(125)[/tex]
[tex]log_{4}(125)= \frac{log 125}{log 4}[/tex]
125 can be written as 5^3
[tex]log_{4}(125)= \frac{log 5^3}{log 4}[/tex]
move the exponent before log
[tex]log_{4}(125)= \frac{3log 5}{log 4}[/tex]
Now use calculator to evaluate the log
[tex]log_{4}(125)=3.48289[/tex]
