If $(6 x - 5) | ln (2 x + 2.3) | = 8 ln (2 x + 2.3)$ , then value of $x$ , is

- \frac{1}{2}

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\frac{13}{20}

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\frac{13}{6}

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- \frac{13}{6}

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Solution

The correct options are
A $- \frac{1}{2}$
B $\frac{13}{6}$
For $ln (2 x + 2.3) > 0$
$x > - \frac{23}{20}$
$| ln 2 x + 2.3 | = ln (2 x + 2.3)$
So $6 x - 5 = 8$
$\Rightarrow$ $x = \frac{13}{6}$ and $\frac{13}{6} > - \frac{13}{20}$
And at $x = - \frac{13}{20}$ both LHS and RHS becomes $0$
For $- \frac{23}{20} < x < - \frac{13}{20}$
$0 < ln (2 x + 2.3) < - \infty$
$∴ 6 x - 5 = - 8$
$∴ x = - \frac{1}{2}$

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\frac{\frac{1}{2} . \frac{2}{2}}{1^{3}} + \frac{\frac{2}{2} . \frac{3}{2}}{1^{3} + 2^{3}} + \frac{\frac{3}{2} . \frac{4}{2}}{1^{3} + 2^{3} + 3^{3}} + . . . .

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