Answer :
Simplify each term.
Simplify 3log(x) by moving 3 inside the logarithm.
log(x^3)+2log(y−1)−5log(x)
Simplify 2log(y−1) by moving 2 inside the logarithm.
log(x^3)+log((y−1)^2)−5log(x)
Rewrite (y−1)^2 as (y−1)(y−1).
log(x^3)+log((y−1)(y−1))−5log(x)
Expand (y−1)(y−1) using the FOIL Method.
log(x^3)+log(y(y)+y(−1)−1(y)−1(−1))−5log(x)
Simplify each term.
log(x^3)+log(y^2−2y+1)+log(x^−5)
Remove the negative exponent by rewriting x^−5 as 1/x^5.
log(x^3)+log(y^2−2y+1)+log(1/x^5)
Combine logs to get log(x^3(y^2−2y+1))
log(x^3(y^2−2y+1))+log(1/x^5)
Combine logs to get log(x^3(y^2−2y+1)/x^5)
log(x^3(y^2−2y+1)/x^5)
Cancel x^3 in the numerator and denominator.
log(y^2−2y+1/x^2)
Rewrite 1 as 1^2.
y^2−2y+1^2/x^2
Factor by perfect square rule.
(y−1)^2/x^2
Replace into larger expression.
log((y−1)^2/x^2)
Simplify 3log(x) by moving 3 inside the logarithm.
log(x^3)+2log(y−1)−5log(x)
Simplify 2log(y−1) by moving 2 inside the logarithm.
log(x^3)+log((y−1)^2)−5log(x)
Rewrite (y−1)^2 as (y−1)(y−1).
log(x^3)+log((y−1)(y−1))−5log(x)
Expand (y−1)(y−1) using the FOIL Method.
log(x^3)+log(y(y)+y(−1)−1(y)−1(−1))−5log(x)
Simplify each term.
log(x^3)+log(y^2−2y+1)+log(x^−5)
Remove the negative exponent by rewriting x^−5 as 1/x^5.
log(x^3)+log(y^2−2y+1)+log(1/x^5)
Combine logs to get log(x^3(y^2−2y+1))
log(x^3(y^2−2y+1))+log(1/x^5)
Combine logs to get log(x^3(y^2−2y+1)/x^5)
log(x^3(y^2−2y+1)/x^5)
Cancel x^3 in the numerator and denominator.
log(y^2−2y+1/x^2)
Rewrite 1 as 1^2.
y^2−2y+1^2/x^2
Factor by perfect square rule.
(y−1)^2/x^2
Replace into larger expression.
log((y−1)^2/x^2)
