Solve for x log6x + log6 (x + 5) = 2

Answer 1

To solve the equation log6x + log6(x + 5) = 2, we can combine the logarithms using the product rule, which states that loga(x) + loga(y) = loga(xy):

log6(x(x + 5)) = 2
log6(x^2 + 5x) = 2

Now, we can rewrite the logarithmic equation in exponential form:

6^2 = x^2 + 5x
36 = x^2 + 5x

Rearrange the equation into a quadratic form:

x^2 + 5x - 36 = 0

Now, we can factor the quadratic equation:

(x + 9)(x - 4) = 0

Setting each factor to zero:

x + 9 = 0 or x - 4 = 0
x = -9 or x = 4

Therefore, the solutions for x are -9 and 4.