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

1 answer:

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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You unfold chicken wire to make a circular pen. The area of the pen is 78.5 square meters. How many meters of chicken wire do yo

Lelu [443]

Circular pen means you are going to use Area = Pi(r^2).

So 78.5 = pi(r^2). Divide by pi on both sides to get r^2 = 78.5/pi. Take the square root of that to get r or radius = approximately 4.99. If you need an exact answer then use $\sqrt{ \frac{78.5}{ \pi } }$ for the next part because you are not done yet.

Plug whatever R you use into the circumference formula of Circumference = 2(pi)(r).

If you use 4.99, you do 2(pi)(4.99) which is approximately 31.35. If you use the exact answer, you do 2(pi)( $\sqrt{ \frac{78.5}{ \pi} }$ ) which gives you approximately 31.41.

Either way you'll need about 31 meters of chicken wire but the 31.40796 or ~31.41 is closer to the exact answer.

8 0

3 years ago

50 points

Leya [2.2K]

Answer:

$\frac{2}{4} inch$