I'm having trouble with this problem: log(x−21)=2−logx, solve for x. I'm coming up with x=−5 but that can't be right.

Janiya Rose

Janiya Rose

Open question

2022-08-17

Having trouble solving log ( x 21 ) = 2 log x for x
I'm having trouble with this problem:
log ( x 21 ) = 2 log x, solve for x
I'm coming up with x = 5 but that can't be right.

Answer & Explanation

Ashlynn Stephens

Ashlynn Stephens

Beginner2022-08-18Added 25 answers

log ( x 21 ) = 2 log x e log ( x 21 ) = e 2 log x x 21 = e 2 e log x x 21 = e 2 x
Can you take it from here? Remember, we must have x > 21, or else log ( x 21 ) will not be defined!
Note: if you're working with log 10 , then simply replace every e with 10, and you're good to go! For any base, log b , you'd use b where I've used e
Samson Kaufman

Samson Kaufman

Beginner2022-08-19Added 1 answers

Assuming that log x = log 10 x, here are the steps
log ( x 21 ) = 2 log x
log ( x 21 ) + log x = 2
log ( x ( x 21 ) ) = 2
10 log ( x ( x 21 ) ) = 10 2
x ( x 21 ) = x 2 21 x = 100
Now just solve the quadratic equation
x 2 21 x 100 = 0
( x 25 ) ( x + 4 ) = 0
Thus the solution is x = 25. We cannot use x = 4 as a solution because log ( 4 ) is undefined. I hope this helps you understand.

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