Numerical answer
If log₂x + log₄x + log₁₆x = 7, find x.
Show answer and solution
Answer: 16
Convert everything to base 2: log₄x = (log₂x)/2 and log₁₆x = (log₂x)/4.
So log₂x × (1 + 1/2 + 1/4) = 7 ⇒ (7/4)·log₂x = 7 ⇒ log₂x = 4 ⇒ x = 2⁴ = 16.
Tip: log_(bⁿ) x = (1/n)·log_b x — bring all logs to the smallest common base.
So log₂x × (1 + 1/2 + 1/4) = 7 ⇒ (7/4)·log₂x = 7 ⇒ log₂x = 4 ⇒ x = 2⁴ = 16.
Tip: log_(bⁿ) x = (1/n)·log_b x — bring all logs to the smallest common base.
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