Question

use rule of logarithms to expand log(x+3)^2/(x-2)(x^2+5)^4

Answer 1

\[\log\frac{ (x+3)^2 }{ ((x-2)(x^2+5)^4 }\]

Answer 2

\(\large \log\frac AB = \log A - \log B\)
\(\large \log AB = \log A + \log B\)
\(\large \log A^n = n \log A\)

Answer 3

so it \[\log(x^2+5)^4+\log(x+3)^2-\log(x-2)\]

Answer 4

or is it \[\log \frac{x^2+5)^4+\log(x+3)^2}{ \log(x-2) }\]

Answer 5

\( \large
\log\frac{ (x+3)^2 }{ ((x-2)(x^2+5)^4 } = \log(x+3)^2 - \{\log ((x-2)(x^2+5)^4 \} = \\ \large
2*\log(x+3) - \{ \log(x-2) + \log(x^2+5)^4\} = \\ \large
2*\log(x+3) - \log(x-2) - 4*\log(x^2+5) \\ \large
\)