A Logarithm Question?

Question

Write 2lnx + (1/3)ln5 - 3ln2 as one logarithm.

I feel like I REALLY should be remembering something but I can't pin it down. Help?

Answer 1

Hi,

You need the following laws of logarithms:

log(xy) = log x + log y

log(x/y) = log x - log y

log(x^n) = n∙log x

Therefore,

2lnx + (1/3)ln5 - 3ln2

= ln(x^2) + ln(5^1/3) - ln(2^3)

= ln(5^1/3 ∙ x^2) - ln(8)

= ln(5^1/3 ∙ x^2 ÷ 8)

You might want to write 5^1/3 as the cube root of 5 (I just can't type it out).  Hope that helps.