Basic Logarithm Equation log_2(x)=log_x(2) Using the change of base theorem: (log(x))/(log(2)) = (log(2))/(log(x)) Multiplied the denominators on both sides: log(x)log(x)=log(2)log(2)

paratusojitos0yx

paratusojitos0yx

Answered question

2022-11-14

Basic Logarithm Equation
log 2 ( x ) = log x ( 2 )
Using the change of base theorem: log ( x ) log ( 2 ) = log ( 2 ) log ( x )
Multiplied the denominators on both sides: log ( x ) log ( x ) = log ( 2 ) log ( 2 )
I kind of get stuck here. I know that you can't take the square root of both sides of the equation, but still, x = 2 seems to be an obvious solution to the equation. I've missed 2 1 or 1 2 as another answer to the equation, which I am struggling to get to.
Any help will be greatly appreciated, thanks in advance.

Answer & Explanation

Kaeden Lara

Kaeden Lara

Beginner2022-11-15Added 23 answers

You have it, actually.
( log ( x ) ) 2 = ( log ( 2 ) ) 2 log ( x ) = ± log ( 2 )
For the " +" case, you've already solved it.
In the " " case, you have log ( x ) = log ( 2 ) = log ( 2 1 ) = log ( 1 2 ), from which you can get x = 1 2
Josie Kennedy

Josie Kennedy

Beginner2022-11-16Added 2 answers

HINT:
x 2 = y 2 x = ± y
and
log 2 = log ( 1 / 2 )

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