Solve equation, and express irrational solution in exact formas a decimal rounded to 3 decimal places. log_2 x^(log_2 x)=4

atestiguoki

atestiguoki

Answered question

2022-08-04

Solve equation, and express irrational solution in exact formas a decimal rounded to 3 decimal places.
log 2 x log 2 x = 4

Answer & Explanation

Dwayne Hood

Dwayne Hood

Beginner2022-08-05Added 10 answers

log A x = x log A APPLY THIS
we will get
log 2 x log 2 x = 4 , now it's base 2 and raise both equationsby 2
( log 2 x ) 2 = 4, take square root both sides
log 2 x = 2, now raise bothside by 2
x=4
imire37

imire37

Beginner2022-08-06Added 8 answers

we have to use some formula to solve the question
(1) log A x = x log A
(2) if l o g x A = y , then A = x y
log 2 x log 2 x = 4
( log 2 x ) log 2 x = ( 2 ) 2
( log 2 x ) ( log 2 x ) = ( 2 ) 2 .............................[Applying formula(1)]
( log 2 x ) 2 = ( 2 ) 2
log 2 x = 2............................[equating the exponentparts]
x = ( 2 ) 2 .............................[applying formula(2)]
= 4
Answer: x =4

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?