The rewritten form of the expression as a single logarithm is; log {(x+3)²(x-2)^5}/(x-7)³(x²).
<h3>What is the rewritten form of the expression?</h3>
The expression given in the task content can be rewritten as a single logarithm by virtue of the laws of logarithms as follows;
2log(x+3)-3log(x-7)+5log(x-2)-log(x^2)
= log(x+3)² - log(x-7)³ +log(x-2)^5-log(x^2)
= log {(x+3)²(x-2)^5}/(x-7)³(x²)
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Distribute invisible-1 to the 2x^2+4x-12
5x^2+3-2x^2-4x+12
group like terms
5x^2-2x^2-4x+3+12
3x^2-4x+15
The equation rx3+1 can be used to solve the problem,and your answer ends up being 7.
Hi there!

We can find the range using completing the square:
y = -x² - 2x + 8
Factor out a -1:
y = -(x² + 2x) + 8
Use the first two terms. Take the second term's coefficient, divide by 2, and square:
y = -(x² + 2x + 1) + 8
Remember to add by 1 because we cannot randomly add an additional number into the equation:
y = -(x² + 2x + 1) + 8 + 1
Simplify:
y = -(x + 1)² + 9
Since the graph opens downward (negative coefficient), the range is (-∞, 9)