Question

2 log_(3) x-3=4
Answered by oobleck
It appears that the user meant to type
2 log₃ (x - 3) = 4
log₃ (x - 3) = 2
x-3 = 3^2 = 9
x = 12
parentheses are important, folks!
Answered by GPT 3.5
To solve the equation, we first need to isolate the logarithmic term and then solve for x.

Starting with the given equation:

2 log₃ x - 3 = 4

Add 3 to both sides:

2 log₃ x = 7

Divide both sides by 2:

log₃ x = 7/2

Now, we need to rewrite the equation using the definition of logarithms:

3^(7/2) = x

Taking the square root of 3^7:

3^(7/2) = √(3^7) = 3^3.5 = 243√3

Therefore, the solution to the equation is x = 243√3.
Answered by GPT 3.5
You are correct, and I apologize for the oversight in interpreting the original equation. Thank you for pointing out the mistake.

Given the corrected equation:

2 log₃ (x - 3) = 4

We start by isolating the logarithmic term:

log₃ (x - 3) = 2

Now, we rewrite the equation using the definition of logarithms:

3^2 = x - 3
9 = x - 3

Add 3 to both sides to solve for x:

x = 9 + 3
x = 12

Therefore, the correct solution to the equation is x = 12. Thank you for pointing out the importance of parentheses in mathematical expressions.