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Question Number 144515 by Khalmohmmad last updated on 26/Jun/21

$$S_{15}-S_{25}=150$$$$S_{30}=?$$

Commented by MJS_new last updated on 27/Jun/21

$$\mathrm{there}\mathrm{are}\mathrm{at}\mathrm{least}3S\mathrm{s}:S_{15},S_{25}\mathrm{and}{S}_{30}.\mathrm{obviously}$$$$S_{25}\mathrm{is}\mathrm{a}S\mathrm{omething}\mathrm{which}\mathrm{we}\mathrm{can}\mathrm{subtract}$$$$\mathrm{from}{S}_{15}.\mathrm{after}\mathrm{the}\mathrm{substraction}\mathrm{all}\mathrm{that}$$$$\mathrm{remains}\mathrm{is}\mathrm{the}\mathrm{number}150.\mathrm{and}{S}_{30}\mathrm{is}\mathrm{a}$$$$\mathrm{lonesome}\mathrm{question}\mathrm{mark}...$$$$\mathrm{may}\mathrm{I}\mathrm{ask}\mathrm{a}\mathrm{similar}\mathrm{question}?$$$$f\left(x\right)-l\left(x\right)=35$$$$p\left(x\right)=?$$$$\mathrm{should}\mathrm{be}\mathrm{as}\mathrm{easy}\mathrm{as}\mathrm{the}\mathrm{above}\mathrm{one}...$$

Answered by ajfour last updated on 26/Jun/21

$$S_{15}-S_{25}=S_{15-25}=S_{-10}$$$$\Rightarrow \frac{1}{S^{10}}=150$$$$hence\frac{1}{S^{30}}={\left(150\right)}^3$$$$\frac{1}{S_{30}}={\left(3\right)}^{150}$$$$obviously{S}_{30}={\left(\frac{1}{3}\right)}^{150}$$

Commented by Dwaipayan Shikari last updated on 26/Jun/21

$$FUN$$

Commented by MJS_new last updated on 27/Jun/21

$$\mathrm{yes}!!!$$$$\mathrm{similar}\mathrm{to}$$$${\log }_{15}x-{\log }_{25}y=150$$$${\log }_{30}\frac{x}{y}=?$$$${\log }_{15}x-{\log }_{25}y={\log }_{15-25}(x-y)={\log }_{-10}\frac{x}{y}$$$$\Rightarrow \frac{1}{{\log }_{10}\frac{y}{x}}=150$$$$\Rightarrow \frac{1}{{\log }_{30}\frac{y}{x}}=3^{150}$$$$\Rightarrow {\log }_{30}\frac{x}{y}=\frac{1}{{150}^3}$$$${\mathrm{let}}^{\prime }\mathrm{s}\mathrm{invent}\mathrm{The}\mathrm{New}\mathrm{World}\mathrm{Mathematics}!$$

Commented by imjagoll last updated on 27/Jun/21

$$\mathrm{hahahaha}.....$$

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