2 log_(3) x-3=4
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.
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!
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.