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umka2103 [35]
3 years ago
6

Information reference tables what is the solution set of the equation log4 (x2 + 3x) − log4 (x + 5) = 1?

Mathematics
1 answer:
faust18 [17]3 years ago
5 0
Use this property of logarithms:

\log_b\left(\dfrac{x}{y}\right)=\log_b x-\log_b y

Your equation transforms into:

log_4\left(\dfrac{x^2+3x}{x+5}\right)=1

Now, you have to apply the definition of a logarithm to express the equation in exponential form:

\dfrac{x^2+3x}{x+5} = 4^1

In case you don't remember, this is the definition of a logarithm:

\log_b x = y \iff b^y = x

The log is the exponent (y) you have to raise the base (b) to in order to get the power (x).

Finally, solve the rational equation:

\dfrac{x^2+3x}{x+5} =4 \iff x^2+3x=4(x+5)
\iff x^2-x-20=0
\iff x=\dfrac{1\pm\sqrt{(-1)^2-4\cdot(-20)}}{2}= \left \{ {{5} \atop {-4}} \right.

The correct answer is d.
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