Numerical answer
If log₃ x + log₉ x + log₂₇ x = 11, find x.
Show answer and solution
Answer: 729
Convert every term to base 3: log₉ x = (log₃ x)/2 and log₂₇ x = (log₃ x)/3.
So log₃ x (1 + 1/2 + 1/3) = 11, i.e. (11/6) log₃ x = 11, giving log₃ x = 6.
x = 3⁶ = 729.
Tip: log_{bⁿ} x = (1/n) log_b x. Always bring logs to a common base first.
So log₃ x (1 + 1/2 + 1/3) = 11, i.e. (11/6) log₃ x = 11, giving log₃ x = 6.
x = 3⁶ = 729.
Tip: log_{bⁿ} x = (1/n) log_b x. Always bring logs to a common base first.
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