log3x^2(x-9)

Question

Write each expression as a sum or difference of multiples of logarithms. Assume that variables represent positive numbers

log3x^2(x-9)

 

What formula do I use for this? Please go step by step. I have an exam soon.

Answer 1

log[(3x²)(x-9)] is I believe the problem you are stating.

 

1st note  log(mn) = log(m) + log(n) so

 

log[(3x2)(x-9)] = log(3x²) + log(x-9)

= log(3) + log(x²) + log(x-9)

 

2nd:  Note log(xⁿ) = nlog(x) so

 

 log(3) + log(x²) + log(x-9) = log(3) + 2log(x) + log(x-9)