Solve the given equation (log3x)2−6(log3x)+9=0
A. 27
B. 9
C. 127
D. 18
E. 81
Let's simplify the equation:
Let's use substitution, let y = log3x.
The equation becomes y^2 - 6y + 9 = 0.
This is a quadratic equation that can be factored as (y - 3)^2 = 0.
This implies y - 3 = 0, so y = 3.
Substituting back, log3x = 3.
3^3 = x.
x = 27.
Therefore, the answer is A. 27.
To solve the given equation, let's first make a substitution. Let's denote u = log3x.
Therefore, the equation becomes:
u^2 - 6u + 9 = 0
Now, we can solve this quadratic equation by factoring:
(u - 3)^2 = 0
Taking the square root of both sides, we have:
u - 3 = 0
u = 3
Now, let's substitute back:
log3x = 3
To get rid of the logarithm, we need to convert the equation into exponential form:
3^3 = x
x = 27
Therefore, the solution to the equation is x = 27.
Answer: A. 27