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3 years ago

The capacity at the local police 225 people

Mathematics

1 answer:

andreyandreev [35.5K]3 years ago

7 0

If they were 19& people at the pool what is the percentage 16.9

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What is the true solution to the equation below?

Marina CMI [18]

Answer:

The solution is:

$x=4$

Step-by-step explanation:

Considering the expression

$lne^{lnx}+lne^{lnx}^{^2}=2ln8$

$\ln \left(e^{\ln \left(x\right)}\right)+\ln \left(e^{\ln \left(x\right)\cdot \:2}\right)=2\ln \left(8\right)$

$\mathrm{Apply\:log\:rule}:\quad \:log_a\left(a^b\right)=b$

$\ln \left(e^{\ln \left(x\right)}\right)=\ln \left(x\right),\:\space\ln \left(e^{\ln \left(x\right)2}\right)=\ln \left(x\right)2$

$\ln \left(x\right)+\ln \left(x\right)\cdot \:2=2\ln \left(8\right)$

$\mathrm{Add\:similar\:elements:}\:\ln \left(x\right)+2\ln \left(x\right)=3\ln \left(x\right)$

$3\ln \left(x\right)=2\ln \left(8\right)$

$\mathrm{Divide\:both\:sides\:by\:}3$

$\frac{3\ln \left(x\right)}{3}=\frac{2\ln \left(8\right)}{3}$

$\ln \left(x\right)=\frac{2\ln \left(8\right)}{3}.....A$

Solving the right side of the equation A.

$\frac{2\ln \left(8\right)}{3}$

$\ln \left(8\right):\quad 3\ln \left(2\right)$

Because

$\ln \left(8\right)$

$\mathrm{Rewrite\:}8\mathrm{\:in\:power-base\:form:}\quad 8=2^3$

⇒ $\ln \left(2^3\right)$

$\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)$

$\ln \left(2^3\right)=3\ln \left(2\right)$

$\frac{2\ln \left(8\right)}{3}=\frac{2\cdot \:3\ln \left(2\right)}{3}$

$\mathrm{Multiply\:the\:numbers:}\:2\cdot \:3=6$

$=\frac{6\ln \left(2\right)}{3}$

$\mathrm{Divide\:the\:numbers:}\:\frac{6}{3}=2$

$=2\ln \left(2\right)$

So, equation A becomes

$\ln \left(x\right)=2\ln \left(2\right)$

$\mathrm{Apply\:log\:rule}:\quad \:a\log _c\left(b\right)=\log _c\left(b^a\right)$

$=\ln \left(2^2\right)$

$=\ln \left(4\right)$

$\ln \left(x\right)=\ln \left(4\right)$

$\mathrm{Apply\:log\:rule:\:\:If}\:\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\:\mathrm{then}\:f\left(x\right)=g\left(x\right)$

$x=4$

Therefore, the solution is

$x=4$

6 0

3 years ago

Read 2 more answers

Equation for motion

AlexFokin [52]

v=at+v^0 is the equation

7 0

3 years ago

urgente ordenar de mas grande a mas pequeño estos numeros: 85,94 85,490 , 85,93, 85,035 ,85

Ilia_Sergeevich [38]

Largest to Smallest:-

First lets write all the numbers down. 45, 94, 85, 490, 85, 93, 85, 035, 85.

035 is 35.

So lets order them now.

The biggest number is 490 and smallest is 35 (035).

490 - 94 - 93 - 85 - 85 - 85 - 85 - 035 (35)

4 0

3 years ago

Read 2 more answers

What answer for not graph just solve it 5x + y = 2

Goryan [66]

Y=2-5x

or

y= .40 - x

6 0

3 years ago

A book is on sale for 30% off. The sale price of the book is $14. What is the original price of the book

Yuki888 [10]

Since $14 is the price after a 30% discount then $14 is 70% of the original price.

$14/70=x/100 (100% would be the original price)

1400=70x or 1400/70 = $20!

You can double check the work by taking 30% off the $20 (10% would be $2, 30% would then be $6) 20-6=14!

8 0

3 years ago