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3 years ago

15

What is a prime number

2 answers:

kolezko [41]3 years ago

6 0

A prime number is a number that can only be divided by 1 by itself

UkoKoshka [18]3 years ago

5 0

Answer:

A prime number is any number that cant be divide by any number but 1 (Ex. 1 2 3 5; Non-Ex. 4 6 8)

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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.

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

As

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

Because

$\ln \left(8\right)$

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

⇒ $\ln \left(2^3\right)$

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

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

So

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

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

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

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

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

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

How many years will it take for $20,000 to earn $7,000 in interest if placed in an account that earns 2.09% simple interest?

aalyn [17]

Answer:

16.7 years

Step-by-step explanation:

7 0

3 years ago

Alexica finds the product, p, of 89 and 35. Which equation justifies her answer? (

Varvara68 [4.7K]

Answer:

hckkcjl4yhjvgvccbjjhjc,zbhbbmk jlkvcuko

5 0

4 years ago

Find the missing length indicated <br> A) 25<br> B) 5<br> C) 8<br> D) 3

Nonamiya [84]

Given:

The figure of a triangle.

To find:

The missing length.

Solution:

Let x be the missing length.

Basic proportionality theorem(BPT): According to this theorem, if a line is parallel to the one side of a triangle then that the line intersects the other two sides of the triangle in the same ratio.

Using Basic proportionality theorem, we get

$\dfrac{6}{8-6}=\dfrac{12-x}{x}$

$\dfrac{6}{2}=\dfrac{12-x}{x}$

$3=\dfrac{12-x}{x}$

$3x=12-x$

Adding x on both sides, we get

$3x+x=12$

$4x=12$

$x=\dfrac{12}{4}$

$x=3$

The missing length is 3 Therefore, the correct option is D.

3 0

3 years ago

Price of 1kg sugar is Rs. 100 calculate the price of 150g sugar?

Wewaii [24]

Answer:Rs15

Step-by-step explanation:

150g=150/1000=0.15kg

1kg cost Rs100

0.15kg cost =100 x 0.15=15

150g cost Rs15

3 0

3 years ago