Solve for X in

(Log X)-6Log X+9=0
³ ³

Solve for X in (log base 3 X)²-6log base 3 X+9=0

if you let u=log_3(x) then you have

u^2-6u+9 = 0
(u-3)^2 = 0
u = 3
so,
log_3(x) = 3
x = 27

To solve the equation (Log X) - 6Log X + 9 = 0, we can use the properties of logarithms.

Step 1: Combine the terms containing Log X.
(Log X) - 6(Log X) + 9 = 0

To combine the terms, we can subtract 6(Log X) from (Log X):
-5(Log X) + 9 = 0

Step 2: Move the constant term to the other side.
-5(Log X) = -9

Step 3: Divide both sides by -5 to isolate the logarithm.
Log X = -9 / -5
Log X = 9/5

Step 4: Rewrite the equation as an exponential equation.
X = 10^(9/5)

So, X equals approximately 74.92.

To solve for X, we can use the property of logarithms, which states that if Log A = B, then A = 10^B. In this case, we have Log X = 9/5, so we can rewrite X as 10^(9/5) to get the approximate value of X.