log-4-5x-6-log-x-256-8-

Question Number 106024 by john santu last updated on 02/Aug/20

\log_{4} (5 x - 6) . \log_{x} (256) = 8

Commented by Dwaipayan Shikari last updated on 02/Aug/20

{2, 3}

Answered by Dwaipayan Shikari last updated on 02/Aug/20

\frac{l o g (5 x - 6) . l o g (256)}{l o g (4) . l o g (x)} = 8

\frac{l o g (5 x - 6) . 8 l o g (2)}{2 l o g (2) l o g (x)} = 8

\frac{l o g (5 x - 6)}{l o g (x)} = 2

5 x - 6 = e^{2 l o g (x)}

5 x - 6 = x^{2}

x^{2} - 5 x + 6 = 0

{\begin{cases} x = 2 \\ x = 3 \end{cases}

Answered by bemath last updated on 02/Aug/20

\frac{1}{2} \times 8 \log_{2} (5 x - 6) . \log_{x} (2) = 8

\log_{2} (5 x - 6) = 2 . \log_{2} (x)

x^{2} - 5 x + 6 = 0

x = 2 & x = 3

Facebook Tweet Pin