NDA 2023 Maths · Mathematics · Logarithms · medium

If log 2x+log 4x+log 16x=7, then x equals

Single correct option

\log_2x+\log_4x+\log_{16}x=7

, then

x

equals

Show answer and solution

Answer: (C) $16$

Express all logarithms in base

2

\log_4x=\frac12\log_2x

and

\log_{16}x=\frac14\log_2x

. The equation becomes

\left(1+\frac12+\frac14\right)\log_2x=7

, so

\log_2x=4

and

x=16

. Adding the bases instead of converting is the common error.

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