Logarithms Logarithms

Question

If ln a=2, ln b=3, and ln c=5, evaluate the following. Give your answer as an integer, fraction, or decimal rounded to at least 4 places. 

1) ln (a^-1/b³c^-4)=

2) ln √ b¹c¹a^-3=

3) ln (a^-2b⁴) / ln (bc)¹=

4) (ln c^-4)(ln a/b^-3)¹⁼

Answer 1

For each problem, first simplify using the rules of logs. For instance, for problem 1 we have

ln(a^-1 / (b³c^-4)) = ln(a^-1) - ln(b³c^-4) = -lna - [ln(b³) + ln(c^-4) = -lna - 3lnb + 4lnc = -2 - 3(3) + 4(5) = 9

The other problems can be done in a similar manner.

Answer 2

In a=2, a=e^x=7.389056.....

ln b=3, b=20.085536.....

ln c=5, c=148.413159.....

Do your substituting.