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Question Number 57368 by problem solverd last updated on 03/Apr/19

$$5^{3x-3}-5^{3x}-5=615$$$$\mathrm{solve}\mathrm{for}x$$

Answered by tanmay.chaudhury50@gmail.com last updated on 03/Apr/19

$$5^{3x}=a$$$$\frac{5^{3x}}{5^3}-5^{3x}-5=615$$$$\frac{a}{125}-a=620$$$$\frac{a-125a}{125}=620$$$$-124a=620\times 125$$$$a=\frac{-620\times 125}{124}=\frac{-5\times 125}{1}=-5^4$$$$5^{3x}=-5^4$$$$hereistheproblemarises..$$$$5^{3x}cannotbenegetive...$$$$$$

Commented by MJS last updated on 04/Apr/19

$$\mathrm{for}x\in \mathbb{C}{\mathrm{we}}^{\prime }\mathrm{d}\mathrm{get}$$$$x=\frac{4}{3}+\frac{2n+1}{3\ln 5}\pi \mathrm{i}\mathrm{with}n\in \mathbb{Z}$$

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