1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ivanshal [37]
3 years ago
5

What is the true solution to the equation below?

Mathematics
2 answers:
Marina CMI [18]3 years ago
6 0

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
Shtirlitz [24]3 years ago
4 0

Answer:

x = 4

Step-by-step explanation:

You might be interested in
Which of the following is a zero of the function F(x)= x³-4x²-7x+10
liubo4ka [24]
The answer is B -4 so ya I think though
7 0
3 years ago
Find the value of y if the line through the two given points is to have the indicated slope.
Masteriza [31]
Slope is the change in y/ change in x so the equation will be:
-2= (1-y)/(-6-(-5)) -> simplify -> -2= 1-y/-1 -> multiply both sides by -1 -> 2=1-y -> simplify and -y= 1 -> y=-1 
4 0
3 years ago
8/21 fraction to decimal ​
katrin [286]

Answer:

Solution and how to convert 8 / 21 into a percentage

0.38 times 100 = 38.1. That's all there is to it!

Step-by-step explanation:

hope this helps

7 0
2 years ago
A concert starts at 7:00 p.M. The chorus performs for 30 minutes. There is a 15-minute break and then the band performs for 30 m
True [87]

Answer:

8:15 pm

Step-by-step explanation:

A concert starts by 7:00pm

They perform for 30 minutes

There is a 15 minutes break

The band performs for another 30 minutes

Hence the concert will end by 8:15 pm

5 0
3 years ago
HELP ROUND 479065.389037 TO THE NEAREST THOUSAND
exis [7]
ROUND 479065.389037 TO THE NEAREST  THOUSAND = <span>479,000</span>
8 0
3 years ago
Read 2 more answers
Other questions:
  • A dealer paid $10000 for a boat at an auction. At the dealership, a salesperson sold the boat for 30% more than the auction pric
    7·1 answer
  • Which is true about the completely simplified difference of the polynomials 6x6 − x3y4 − 5xy5 and 4x5y + 2x3y4 + 5xy5?
    12·2 answers
  • A quadratic function and an exponential function are graphed below. Which graph most likely represents the exponential function?
    9·2 answers
  • Which mixed number is equal to 6.75?
    9·2 answers
  • Three times a number plus 12 minus 5 times the same number is 22
    10·2 answers
  • Whats the 32nd Term of the sequence 34,37,40,43
    10·1 answer
  • Which answers describe the shape below? Check all that apply.
    14·1 answer
  • If $5000 is deposited at the beginning of every six months into an account that earns 8% compounded semiannually find the amount
    14·1 answer
  • IXL- 8th grade math W.14
    10·2 answers
  • Find the area and perimeter of the original planned patio and the new planned patio? help me please​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!