3logX - log6 + log2.4 = 9

To solve the equation 3logX - log6 + log2.4 = 9, we need to use properties of logarithms to simplify the equation and isolate the variable X.

Step 1: Combine the logarithms using logarithmic properties.
Using the properties of logarithms, we can rewrite the equation as a single logarithm:
logX^3 - log6 + log2.4 = 9

Step 2: Apply the rules of logarithms to simplify the equation.
By applying the rule of logarithms, log(a) + log(b) = log(ab), we can combine the logs:
log[(X^3 * 2.4) / 6] = 9

Step 3: Convert the logarithmic equation into an exponential equation.
Using the definition of logarithms, log(base b) (x) = y is equivalent to b^y = x, we can rewrite the equation:
10^9 = (X^3 * 2.4) / 6

Step 4: Simplify the equation further.
Multiply both sides of the equation by 6 to eliminate the denominator:
6 * 10^9 = X^3 * 2.4

Step 5: Divide both sides of the equation by 2.4 to isolate X^3:
(6 * 10^9) / 2.4 = X^3

Step 6: Calculate the value of X.
Now, we take the cube root of both sides to solve for X:
X = ∛[(6 * 10^9) / 2.4]

Using a calculator, we can evaluate the expression on the right-hand side to find the value of X.