Question

suppose that In 2 = a and In 3 = b. Use properties of logarithms to write each logarithm in terms of a and b. I need help with number 39 and 43. I am confused on how to get the answer. Thanks for your help!

Answer 1

we are given

$a=ln(2)$

$b=ln(3)$

(39)

$ln(6)$

we can write it as

$ln(6)=ln(2*3)$

now, we can use property of log

$ln(6)=ln(2)+ln(3)$

now, we can replace with a and b

and we get

$ln(6)=a+b$............Answer

(43)

$ln(9)$

we can write it as

$ln(9)=ln(3^2)$

now, we can use property of log

$ln(9)=2ln(3)$

now, we can replace with a and b

and we get

$ln(9)=2b$............Answer