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katen-ka-za [31]
3 years ago
5

Topics in math question

Mathematics
1 answer:
Monica [59]3 years ago
5 0

Answer:24

Step-by-step explanation:

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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
Find the measures of the angles of a right triangle where one of the two acute angles measure 8 times the otehr.
Goryan [66]

Answer:

Step-by-step explanation:

The two acute angles add up to 90 degrees. That's because every triangle has 180 degrees and a right angle is 90 degrees.

<m1 + <m2 + 90 = 180                   Subtract 90 from both sides.

<m1 + <m2 + 90 - 90 = 180 - 90   Combine

<m1 + <m2 = 90

Let m1 = 9*m2                                Substitute.

9m2 + m2 = 90                              Combine

10 m2 = 90                                     Divide by 10

10m2/10 = 90/10

m2 = 9

m1 = 9*m2

m1 = 9 * 9

m1 = 81

The right angle = 90

m1 = 81

m2 = 9

8 0
3 years ago
What is the slope of 6x-3y=18??
dolphi86 [110]
the \ slope \ intercept \ form \ is : \\  \\ y= mx +b \\ \\6x-3y=18 \\ \\-3y=-6x+18 \ \ /:(-3)\\ \\y=\frac{-6}{-3}x + \frac{18}{-3} \\ \\y=2x-6 \\ \\ m = 2
6 0
3 years ago
How do you sole this question kelpie sold cameras on her web site. She bought the cameras for $65 each included a 60% markup to
postnew [5]
So 65 dollars was what she paid
each camera INCLUDED a 60% mark UP so
she sold each at a 60% markup

65 dollars=100% of origonal camers
she sold them for 100+60=160% of origonal price
65 dollars=100%
percent means parts out of 100 so
160%=160/100=1.6

find 160% of 65
'of' means multiply so
1.6 times 65=104

she sold each camera at $104
4 0
3 years ago
Define perpendicular bisector​
tresset_1 [31]

Answer:

Step-by-step explanation:

A perpendicular bisector is a special kind of segment, ray, or line that. (1) intersects a given segment at a 90° angle, and. (2) passes through the given segment's midpoint. Segment CD is the perpendicular bisector to segment AB. We derive two important theorems from the characteristics of perpendicular bisectors.

7 0
3 years ago
Read 2 more answers
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