use the laws of logarithms to express each given natural log

use the laws of logarithms to express each given natural logarithm in terms of just the three natural logarithms ln 2, ln 3, ln 5.

a. ln 8

b. ln 15

c. ln 9/25

d. find the approx value of ln 25 rounded to 4 decimal places by solving the equation e^x=25 graphically.

Use following log properties:

lna^x = x*lna

lnA*B = lnA +lnB

ln(A/B) = lnA - lnB

a) ln8 = ln(2^3) = 3*ln2

b) ln(15) = ln(3*5) = ln3 +ln5

c) ln(9/25) = ln(3^2/5^2) = ln(3/5)^2 = 2ln(3/5) = 2[ ln3 - ln5]

d) value of ln(25)

e^x = 25

take ln of both sides:

ln(e^x) = 25

x*lne = ln25

x = ln25