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3 years ago

Evaluate the logarithmic function for the given value.

Mathematics

1 answer:

STALIN [3.7K]3 years ago

5 0

Answer:

$f(125) = log_{5}(125 ) \\ = log_{5}( {5}^{3} ) = 3 log_{5}(5 ) = 3(1) = 3$

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$\frac{{y}^{2}+13y-6}{{(y-1)}^{2}(y+7)}$

Step-by-step explanation:

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$\frac{y}{{y}^{2}-2(y)(1)+{1}^{2}}+\frac{6}{{y}^{2}+6y-7}$

2) Use Square of Difference: ${(a-b)}^{2}={a}^{2}-2ab+{b}^{2}$ .

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3) Factor ${y}^{2}+6y-7$ .

1 - Ask: Which two numbers add up to 6 and multiply to -7?

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2 - Rewrite the expression using the above.

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Outcome/Result: $\frac{y}{(y-1)^2} +\frac{6}{(y-1)(y+7)}$

4) Rewrite the expression with a common denominator.

$\frac{y(y+7)+6(y-1)}{{(y-1)}^{2}(y+7)}$

5) Expand.

$\frac{{y}^{2}+7y+6y-6}{{(y-1)}^{2}(y+7)}$

6) Collect like terms.

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$\frac{{y}^{2}+13y-6}{{(y-1)}^{2}(y+7)}$

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2 years ago

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