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Logarithmic Differentiation

Solve the fol...

Question

Solve the following equation:
$\frac{1}{2} log (5 x - 4) + log \sqrt{x + 1} = 2 + log 0.18$

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Solution

$\frac{1}{2} l o g (5 x - 4) + l o g \sqrt{x + 1} = 2 + l o g (0.18) \Rightarrow l o g (5 x - 4) + 2 l o g \sqrt{x + 1} = 2 [2 + l o g (0.18)] \Rightarrow (5 x - 4) (x + 1) = 324 \Rightarrow {5 x}^{2} + 4 x - 328 = 0 \Rightarrow {5 x}^{2} + 41 x - 40 x - 328 = 0 \Rightarrow x (5 x + 41) - 8 (5 x + 41) = 0 \Rightarrow x = 8, \frac{- 41}{3} .$

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