The solution of the given logarithmic equation log₆ x + log₆ (x + 5) = 2 is
x = - 9, 4.
What is logarithm?
"The logarithm is the inverse function to exponentiation. That means the logarithm of a given number 'x' is the exponent to which another fixed number, the base 'b', must be raised, to produce that number 'x'."
The given logarithmic equation is:
log₆ x + log₆ (x + 5) = 2
⇒ log₆ x(x + 5) = 2log₆ 6
⇒ log₆ x(x + 5) = log₆ (6)²
⇒ log₆ x(x + 5) = log₆ 36
⇒ x(x + 5) = 36
⇒ x² + 5x - 36 = 0
⇒ x² + 9x - 4x - 36 = 0
⇒ x(x + 9) - 4(x + 9) = 0
⇒ (x + 9)(x - 4) = 0
⇒ x = - 9, 4
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