O lvl A Maths: Indices and Logarithms

Solve the equation log₃ 2 + log₃(x + 4) = 2 log₃ x.

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Answer:

log₃ 2 + log₃(x + 4) = 2 log₃ x
log₃ 2 (x + 4) = log₃ x²
2 (x + 4) = x²
x² - 2x - 8 = 0
(x - 4)(x + 2) = 0
x = 4 or -2

For log₃ x to be defined, x = 4.

Note: x = -2 is rejected because log₃ x will be undefined.