Tabansi

## Answered question

2021-05-22

$\left(\frac{{10}^{x}-\left({10}^{-x}\right)}{11}=12\right).$

### Answer & Explanation

Szeteib

Skilled2021-05-23Added 102 answers

$\left(\frac{{10}^{x}-\left({10}^{-x}\right)}{11}=12\right).$
$\left(\left({10}^{x}-\left({10}^{-x}\right)\right)\cdot 11=12\cdot 11$
$\left({10}^{x}\right)-\left({10}^{-x}\right)=132$
${10}^{x}-{\left({10}^{x}\right)}^{-1}=132$
Rewrite the equation with ${10}^{x}=u$
$u-{\left(u\right)}^{-1}=132$
$u-\left(\frac{1}{u}\right)=132$
$u-\left(\frac{1}{u}\right)u=132u$
${u}^{2}-1=132u$
${u}^{2}-132u-1=0$
$u=66+\sqrt{4357},u=66-\sqrt{4357}$
Substitute back $u={10}^{x}$, solve for x
Solve ${10}^{x}=66+\sqrt{4357};x=\frac{\mathrm{ln}\left(66+\sqrt{4357}\right)}{\mathrm{ln}\left(10\right)}$
Solve ${10}^{x}=66-\sqrt{4357}$; No Solution for $x\in Rx=\left(\mathrm{ln}\left(66+\sqrt{4357}\right)\right)/\mathrm{ln}\left(10\right)$

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