Question 756076
You only need 3 rules:
(1) {{{ log(a) + log(b) = log(a*b) }}}
(2) {{{ log(a) - log(b) = log(a/b) }}}
(3) {{{ b*log(a) = log( a^b) }}}
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{{{ 4*log( x ) - 2*log(x^2+1) + 3*log(x-1) }}}
Rewrite the order of the terms:
{{{ 4*log( x ) + 3*log(x-1) - 2*log(x^2+1) }}}
Apply rule 3
{{{ log( x^4 ) + log( ( x-1 )^3 ) - log( ( x^2 + 1 )^2) }}}
Apply rules 1 and 2
{{{ log(( x^4 * ( x-1)^3 )) - log(( ( x^2 + 1 )^2)) }}}
{{{ log(( x^4 * ( x-1)^3 ) / ( x^2 + 1 )^2 )) }}}
{{{ log(( x^4 * ( x-1)^3 ) / ( x^2 + 1 )^2 )) }}}
I could expand everything, but that's not needed.