Answer:
1. 1.685
2. 16.828
Step-by-step explanation:
1. log_5 15
To evaluate this logarithm you use the following formula:
[tex]Log_ab=\frac{log_{10}b}{log_{10} a}[/tex]
by replacing you obtain:
[tex]log_5 15=\frac{log_{10} 15}{log_{10}5}=\frac{1.176}{0.698}=1.685[/tex]
hence, the answer is 1.685
2. -3ln(1/e4/5)
to solve this logarithm you use the following properties:
[tex]ln(a^m)=m\ ln(a)\\\\ln(\frac{a}{b})=ln(a)-ln(b)\\\\ln(e^m)=m[/tex]
[tex]ln(1)=0[/tex]
By applying all these properties you obtain:
[tex]-3ln(\frac{1}{\frac{e^4}{5}})=-3[ln(\frac{1}{e^4})-ln(5)]=-3[ln(1)-ln(e^4)-ln(5)]\\\\-3ln(\frac{1}{\frac{e^4}{5}})=-3[0-4-1.609]=16.828[/tex]
hence, the answer is 16.282
