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>
Answer:
752
Step-by-step explanation:
IN these type of questions we put the numbers in descending order
I believe the answer is B
Answer:
6 hours 26 minutes
Step-by-step explanation:
So 15 gallons of gas brought it from 1/8 full to 3/4 full.
Let's change 3/4 to the equivalent fraction 6/8 so that the denominators are the same. (3/4 = 6/8)
So 15 gallons of gas brought it from 1/8 to 6/8 Those 15 gallons must be 5/8 of the tank's capacity 6/8 - 1/8 = 5/8
So 15 is 5/8 of what number? (This will tell us the capacity of the whole tank)
15 = 5/8n
Divide both sides by 5/8 (remembering to multiply by the reciprocal 8/5)
15 ÷ 5/8 = 15 x 8/5 = 18
So the tank holds 24 gallons and (since it is 3/4 full or has 18 gallons) it needs 6 gallons to fill the tank.
Check - at first 1/8 full (1/8 of 24 = 3) So we started with 3 gallons. 15 gallons added to the 3 gallons is 18 gallons. Now the tank is 6/8 (3/4 full). The remaining 1/4 (2/8) of a tank is the difference between 18 and it's capacity (24 gallons) so it will need 6 gallons to fill it up..
