Solve the logarithmic equation .

Question

Solve the logarithmic equation  . ​

Quizplus · Accepted Answer

We have:
log(base 3)x + log(base 3)(x+4) = 2
Applying the product rule of logarithms:
log(base 3)(x(x+4)) = 2
Rewriting in exponential form:
3^2 = x(x+4)
Simplifying:
9 = x^2 + 4x
Re-arranging:
x^2 + 4x - 9 = 0
Using the quadratic formula:
x = (-4 ± sqrt(4^2 - 4(1)(-9))) / (2(1))
x = (-4 ± sqrt(52)) / 2
x = (-4 ± 2sqrt(13)) / 2
x = -2 ± sqrt(13)
Since the question asks for the product of the solutions, we multiply:
(-2 + sqrt(13))(-2 - sqrt(13)) = (4 - 13) / (1) = -9
Therefore the answer is -9.

Solve the Logarithmic Equation . ​

Solve the Logarithmic Equation .