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3 years ago

Step by step workout of ; log x^3+log 5x=5 log 2-log 2/5

Mathematics

1 answer:

Charra [1.4K]3 years ago

4 0

Answer:

x = 2

Step-by-step explanation:

$log \: {x}^{3} + log \: 5x = 5log \: 2 - log \: \frac{2}{5} \\ \\ \therefore \: log( {x}^{3} \times 5x) = log {2}^{5} - log \: \frac{2}{5} \\ \\ \therefore \: log( 5{x}^{4}) = log 32 - log \: \frac{2}{5} \\ \\ \therefore \: log( 5{x}^{4}) = log \bigg(32 \times \frac{5}{2} \bigg) \\ \\ \therefore \: log( 5{x}^{4}) = log \bigg(16 \times 5) \\ \\ \therefore \: 5{x}^{4}= 16 \times 5 \\ \\ \therefore \: {x}^{4}= {2}^{4} \\ \\ \huge \purple{ \boxed{\therefore \: {x} = 2}}$

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3 years ago

Please help me with this geometry problem. :)

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Answer:

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Step-by-step explanation:

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2 years ago

What is the answer to 8(x-3)+7=2x(4-17)

nadezda [96]

Answer:

x=1/2

Step-by-step explanation:

First you distribute the 8 over the (x-3) giving you 8x-24. Do the same for 2x and (4-17). That should give you 8x-34x.

Your equation should look like : 8x-24+7=8x-34x

Next try to balance out your equation. You want your x's all by themselves in order to solve.

The 8x's cancel eachother out so you have -24+7= -34x.

Add the like terms of -24 and 7 to get -17.

Equation: -17= -34x

Divide both sides by -34 to get x by itself.

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3 years ago

In the diagram below,AB is the diameter of the circle with centre P.Point C lies on the y-axis.Given the coordinates of A and B

Step2247 [10]

Answer:

The coordinates of P are (-2,0)

The radius of the circle is 5.

Step-by-step explanation:

Analytic geometry

The diagram shows a circle with center P, and two points A(-6,3) and B(2,-3) that form the diameter of the circle.

The center of the circle lies at the midpoint of A and B. The midpoint (xm,ym) can be calculated by:

$\displaystyle x_m=\frac{x_1+x_2}{2}$

$\displaystyle y_m=\frac{y_1+y_2}{2}$

Substituting x1=-6, x2=2, y1=3, y2=-3:

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Thus, the coordinates of P are (-2,0)

b) The radius of the circle is the distance from the center to any point in its circumference. We can use the distance from P to A or B indistinctly.

Given two points A(x1,y1) and P(x2,y2), the distance between them is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substituting x1=-6, x2=-2, y1=3, y2=0:

$r=\sqrt{(-2+6)^2+(0-3)^2}$

$r=\sqrt{4^2+(-3)^2}$

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3 years ago

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3 years ago

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