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