Question

Write expression as one logarithm and simplify if appropriate.

log 3√x + log x^4 - log x^3

4 log (x+3) - 5 log (x^2+4) + 1/3 log y

I have these who problems but I don't know where to start. HELP Please.

Answer 1

You are going to use 3 man rules of logs

1. log(A/B) = logA - logB
2. Log(AB) = logA + logB
3. log A^n = nlogA

log 3√x + log x^4 - log x^3
= log 3 + log x^(1/2) + 4logx - 3logx
= log3 + (1/2)logs + logx
= log3 + (3/2)logx

2.

4 log (x+3) - 5 log (x^2+4) + 1/3 log y
= log (x+3)^4 - log (x^2+4)^5 + log y^(1/3)

= log [ y^(1/3) (x+3)^4 /(x^2+4)^5 ]