Question

Let ln2=a, ln3=b, and ln5=c. Express the following logarithms in terms of abc .

ln800=

ln0.096= a+a+b-3c

ln0.027= 3b-(3a+3c)

log2 27000= (3a+3b+3c)/a

Cant find ln800

Answer 1

Find the prime factors of 800 first.

Answer 2

1# setting 800 = 2^5 * 5^2
so, ln800 = ln(2^5 * 5^2) = ln(2^5) + ln(5^2) = 5ln2 + 2ln5 = 5a + 2c

Answer 3

Yeah I just got it as you guys replied. Thanks though!