Remove parentheses<span> in </span>numerator<span>. </span><span>1(log(<span>1/1000</span>x<span>y^2</span>))
</span>The logarithm<span> of a </span>product<span> is equal to the </span>sum<span> of the </span>logarithms<span> of each </span>factor <span>(e.g.</span><span><span>log(xy)=log(x)+log(y)</span>).</span><span> The </span>logarithm<span> of a </span>division<span> is equal to the </span>difference<span> of the </span>logarithms<span> of each </span>factor <span>(e.g.</span><span><span>log(<span>x/y</span>)=log(x)−log(y)</span>). </span><span>1(log(x)+log(<span>y^2</span>)−log(1000))
</span>The exponent<span> of a </span>factor<span> inside a </span>logarithm<span> can be expanded to the front of the </span>expression<span> using the third law of </span>logarithms<span>. The third law of </span>logarithms<span> states that the </span>logarithm<span> of a </span>power<span> of </span>x<span> is equal to the </span>exponent<span> of that </span>power<span> times the </span>logarithm<span> of </span>x<span>(e.g.</span><span><span>lo<span>g^b</span>(<span>x^n</span>)=nlo<span>g^b</span>(x)</span>).
</span><span>log(x)+1((2log(y)))−log(1000)
</span>Remove the extra parentheses<span> from the </span>expression <span><span>1((2log(y)))</span>. </span><span>log(x)+2log(y)−log(1000)
</span>The logarithm base 10<span> of </span>1000<span> is </span><span>3. </span><span>log(x)+2log(y)−((3))
Your answer is -5. This is because, if you expand the single bracket, you get -6x -3a, and since the other side of the equals sign is -6x + 15, then you need to do 15 ÷ -3 = -5.
