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1 year ago

Expand each logarithm. log₄5 x

Mathematics

1 answer:

Romashka [77]1 year ago

5 0

If the expression is log₄5 x,then the expansion of this will look like

(log 5+ log x)/log 4.

Given that the expression is log₄5 x.

We are required to find the expansion of the expression.

Base change theorem says that $log_{a}b$ = $log_{x}b/log_{x}a$ . We use the change of base formula to re-write a logarithm operation as a fraction of logarithms with a new base.

The expression is log₄5 x.

log₄5 x=(log 5+log x)/log 4

(We know that $log_{a}b$ = log b/ log a and log mn =log m +log n)

Hence if the expression is log₄5 x then the expansion of this will look like (log 5+ log x)/log 4.

Learn more about base change theorem at brainly.com/question/14998693

#SPJ4

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Find the value of the variable y, where the sum of the fractions 6/(y+1) and y/(y-2) is equal to their product.

Blizzard [7]

Answer:

The answer is

$y = 3$

$y = - 4$

Step-by-step explanation:

We must find a solution where

$\frac{6}{y + 1} + \frac{y}{y - 2} = \frac{6}{y + 1} \times \frac{y}{y - 2}$

Consider the Left Side:

First, to add fraction multiply each fraction on the left by it corresponding denomiator and we should get

$\frac{6}{y + 1} \times \frac{y - 2}{y - 2} + \frac{y}{y - 2} \times \frac{y + 1}{y + 1}$

Which equals

$\frac{6y - 12}{(y -2) (y + 1)} + \frac{ {y}^{2} + y }{(y - 2)(y + 1)}$

Add the fractions

$\frac{y {}^{2} + 7y - 12 }{(y - 2)(y + 1)} = \frac{6}{y + 1} \times \frac{y}{y - 2}$

Simplify the right side by multiplying the fraction

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

Set both fractions equal to each other

$\frac{6y}{(y + 1)(y - 2)} = \frac{ {y}^{2} + 7y - 12}{(y + 1)(y - 2)}$

Since the denomiator are equal, we must set the numerator equal to each other

$6y = {y}^{2} + 7y - 12$

$= {y}^{2} + y - 12$

$(y + 4)(y - 3)$

$y = - 4$

$y = 3$

6 0

2 years ago

Read 2 more answers

Draw 8 lines that are between 1 inch and 3 inches long. Measure each line to the nearest fourth inch, and make a line plot.

IRISSAK [1]

The length of the line is the difference between the endpoints of the line

The length of each line to the nearest fourth inch is 0.25 inch

<h3>How to measure the length of each line</h3>

The length of the horizontal line is given as:

Length = 2 inches

This is calculated as:

Length = 3 inches - 1 inch

Length = 2 inches

8 lines are to be drawn between the 1 inch and 3 inches point.

So, the length (l) of each line is:

$l = \frac{2\ inches}{8}$

Simplify the fraction

$l = \frac{1\ inches}{4}$

Divide

$l = 0.25\ inch$

Hence, the length of each line to the nearest fourth inch is 0.25 inch

Read more about line measurements at:

brainly.com/question/14366932

6 0

1 year ago

A car is on a driveway that is inclined 10 degrees to the horizontal. A force of 490 lb is required to keep the car from rolling

lara31 [8.8K]

Answer:

a) weight of the car = 2816,1 lbs

b) 2773 lbs

Step-by-step explanation:

The equilibrium force is 490 lbs. That force keep the car at rest, then

∑ Fy = 0 and ∑Fx = 0

Forces acting on the car:

The external force 490 lbs

weight of the car uknown

Normal force

sin∠10° = 0,174

cos∠10° = 0.985

∑Fx = 0 mg*sin10°- 490 = 0 ∑Fy = 0 mg*cos10° - N = 0

mg*0,174= 490

mg = 490 / 0,174

mg = 2816,1 lbs

weight of the car = 2816,1 lbs

The Normal force

mg*cos10° - N = 0 2816,1 * 0,985 = N

N = 2773 lbs

Then equal force in magnitude and in opposite direction will car exets on the driveway

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2 years ago

A museum worker randomly displays 5 historical writings in a row. What is the probability that the worker lines them up from the

Mars2501 [29]

The number of ways to arrange the 5 writings in a row is 5! = 5 * 4 * 3 * 2 * 1 = 120 ways.

There is only 1 way to arrange the writings from oldest to newest.

Therefore, the probability is 1/120.

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2 years ago

Yes or no??<br> math workk

snow_lady [41]

Answer:

Yes, and if you need extra help try yay math

Step-by-step explanation:

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2 years ago