Answer:
Step 1: Simplify the logarithmic expressions.
log_x(27) = log_x(3^3) = 3 (Using the power rule of logarithms)
log_9(x) = 1 / log_x(9) (Using the change of base formula)
Step 2: Substitute the simplified expressions into the equation.
(x^2) * 3 * (1 / log_x(9)) = x + 4
Step 3: Rearrange the equation to isolate the logarithmic term.
(x^2) * 3 = (x + 4) * log_x(9)
Step 4: Raise both sides to the power of x to eliminate the logarithm.
(x^2 * 3)^x = 9^(x + 4)
Step 5: Simplify the expressions using the power rules.
3^(x^2 * x) = 9^(x + 4)
Step 6: Apply the property of logarithms: log_a(b^c) = c * log_a(b)
x^2 * x * log_e(3) = (x + 4) * log_e(9)
Step 7: Substitute the known values of log_e(3) and log_e(9).
x^2 * x * 1.0986 = (x + 4) * 2.1972
Step 8: Simplify the equation and solve for x.
x^3 * 1.0986 = 2.1972x + 8.7888
x^3 - 2x - 8 = 0
Step-by-step explanation:
