The potential solutions of log₆x + log₆(x + 5) = 2 are x = 4 and x = -9
The equation is given as
log₆x + log₆(x + 5) = 2
Apply the product law of logarithm
log₆(x * (x + 5)) = 2
This gives
log₆(x^2 + 5x) = 2
Express as an exponent
x^2 + 5x = 6^2
x^2 + 5x = 36
Rewrite as:
x^2 + 5x - 36 = 0
Expand
x^2 + 9x - 4x - 36 = 0
Factorize
x(x + 9) - 4(x + 9) = 0
This gives
(x - 4)(x + 9) = 0
Solve for x
x = 4 or x = -9
Hence, the potential solutions of log₆x + log₆(x + 5) = 2 are x = 4 and x = -9
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