Solve this logarithmic equation: 2^(2- ln x)+2^(2+ ln x)=8

Aarav Atkins 2022-10-22 Answered
Solve this logarithmic equation: 2 2 ln x + 2 2 + ln x = 8. I thought to write
2 2 2 ln ( x ) + 2 2 2 ln ( x ) = 2 3 2 2 + 2 2 ( 2 ln ( x ) ) 2 2 ln ( x ) = 2 3
What should I do else?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

wespee0
Answered 2022-10-23 Author has 15 answers
We have 2 2 ln ( x ) = 4 2 ln ( x ) and 2 2 + ln ( x ) = 4 2 ln ( x ) . Hence, setting 2 ln ( x ) = a, we obtain
4 a + 4 a = 8 a 2 + 1 = 2 a a = 1 2 ln ( x ) = 1 x = 1
Did you like this example?
Subscribe for all access
Maribel Vang
Answered 2022-10-24 Author has 2 answers
Hint:
Dividing by 4 we get the equivalent equation
2 ln x + 2 ln x = 2
then let y = 2 ln x so
y 1 + y = 2 1 + y 2 = 2 y
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-10-17
What is the reason to introduce and study logarithmic functions?
I don't understand why logarithms exist when we have exponential functions. Exponential functions seem to be an easier and less convoluted way to write something. Why invent logarithms to do something that exponents already do just fine.
asked 2022-10-14
Help with Evaluating a Logarithm
A precalculus text asks us to evaluate log 8 2 256 3 32 6
I do the following: log 8 2 ( 2 2 ) 3 2 2 3 2 3 2 2 6
log 8 2 2 2 2 2 3 2 2 2 6
log 8 2 2 2 2 3 2 3
and then I'm stumped.
Hints?
asked 2021-10-20
Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places log40.863
asked 2022-05-21
Find the domain of g ( x ) = ln ( x x 1 )
I know the argument of the function has to be greater than 0, so:
( x x 1 ) > 0 x > 0
however in this case x 1, x 0 as they result in an answer which is undefined, so I think it's reasonable for me to say the domain is x > 1, however this is not the correct answer.
asked 2022-10-30
Equation in Logarithm
We have
log 4 5 = a
log 5 6 = b
and we have to find log 3 2
I tried the question but because of the different bases I was not able to get the solution.
asked 2022-03-08
Write each expression as a sum and/or difference of logarithms. Express powers as factors.
1.log5(25x)
2.log3x9
asked 2022-05-19
Solve for: 8 log 4 x 2 9 + 3 2 log 4 ( x + 3 ) 2 = 10 + log 2 ( x 3 ) 2
My try:
8 log 4 x 2 9 + 3 2 log 4 ( x + 3 ) 2 = 10 + log 2 ( x 3 ) 2 log 2 ( x 2 9 ) 2 + 3 log 2 ( x + 3 ) 2 = 10 + log 2 ( x 3 ) 2 log 2 ( x 3 ) 2 + log 2 ( x + 3 ) 2 + 3 log 2 ( x + 3 ) 2 10 log 2 ( x 3 ) 2 = 0 log 2 ( x + 3 ) 2 + 3 log 2 ( x + 3 ) 2 10 = 0
But I don't know Conditions defined for this math? Could you help me please?