log-3-x-1-log-4-x-8-x-

Question Number 145067 by imjagoll last updated on 02/Jul/21

\log_{3} (x + 1) = \log_{4} (x + 8)

x = ?

Answered by bobhans last updated on 02/Jul/21

x = 8 \Rightarrow \log_{3} (8 + 1) = \log_{4} (8 + 8)

\Rightarrow 2 = 2

Commented by bobhans last updated on 02/Jul/21

let \log_{3} (x + 1) = k \Rightarrow x + 1 = 3^{k}

and \log_{4} (x + 8) = k \Rightarrow x + 8 = 4^{k}

\Rightarrow 4^{k} - 3^{k} = 7

k = 0 \Rightarrow 1 - 1 \neq 7

k = 2 \Rightarrow 16 - 9 = 7 then x = 3^{2} - 1 = 8 or

x = 4^{k} - 8 = 16 - 8 = 8

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