SOLUTION: 2log x -log3 =log3

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Question 1179950: 2log x -log3 =log3
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
i get x = 3.

start with 2 * log(x) - log(3) = log(3)

add log(3) to both sides of the equation to get:

2 * log(x) = log(3) + log(3)

combine like terms to get:

2 * log(x) = 2 * log(3)

divide both sides by 2 to get:

log(x) = log(3)

this is true if and only if x = 3.

you get:

2 * log(3) - log(3) = log(3)

another way to do it is:

start with 2 * log(x) - log(3) = log(3)

add log(3) to both sides to get:

2 * log(x) = log(3) + log(3)

since log(3) + log(3) = log(3 * 3) which is equal to log(3^2), this becomes:

2 * log(x) = log(3^2)

since 2 * log(x) = log(x^2), this becomes:

log(x^2) = log(3^2)

this is true if and only if x^2 = 3^2

simplify to get x^2 = 9

take the sqare root of both sides of this eqution to get:

x = plus or minus 3.

x can't be -3 because log of a negative number is not real, therefore x = 3.

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!

2log x -log3 =log3

However, x CANNOT be < 0, so