Question Number 144515 by Khalmohmmad last updated on 26/Jun/21
$${S}_{\mathrm{15}} −{S}_{\mathrm{25}} =\mathrm{150} \\ $$$${S}_{\mathrm{30}} =? \\ $$
Commented by MJS_new last updated on 27/Jun/21
$$\mathrm{there}\:\mathrm{are}\:\mathrm{at}\:\mathrm{least}\:\mathrm{3}\:{S}\mathrm{s}:\:{S}_{\mathrm{15}} ,\:{S}_{\mathrm{25}} \:\mathrm{and}\:{S}_{\mathrm{30}} .\:\mathrm{obviously} \\ $$$${S}_{\mathrm{25}} \:\mathrm{is}\:\mathrm{a}\:{S}\mathrm{omething}\:\mathrm{which}\:\mathrm{we}\:\mathrm{can}\:\mathrm{subtract} \\ $$$$\mathrm{from}\:{S}_{\mathrm{15}} .\:\mathrm{after}\:\mathrm{the}\:\mathrm{substraction}\:\mathrm{all}\:\mathrm{that} \\ $$$$\mathrm{remains}\:\mathrm{is}\:\mathrm{the}\:\mathrm{number}\:\mathrm{150}.\:\mathrm{and}\:{S}_{\mathrm{30}} \:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{lonesome}\:\mathrm{question}\:\mathrm{mark}... \\ $$$$\mathrm{may}\:\mathrm{I}\:\mathrm{ask}\:\mathrm{a}\:\mathrm{similar}\:\mathrm{question}? \\ $$$${f}\left({x}\right)−{l}\left({x}\right)=\mathrm{35} \\ $$$${p}\left({x}\right)=? \\ $$$$\mathrm{should}\:\mathrm{be}\:\mathrm{as}\:\mathrm{easy}\:\mathrm{as}\:\mathrm{the}\:\mathrm{above}\:\mathrm{one}... \\ $$
Answered by ajfour last updated on 26/Jun/21
$${S}_{\mathrm{15}} −{S}_{\mathrm{25}} ={S}_{\mathrm{15}−\mathrm{25}} ={S}_{−\mathrm{10}} \\ $$$$\Rightarrow\:\:\frac{\mathrm{1}}{{S}^{\:\mathrm{10}} }=\mathrm{150} \\ $$$${hence}\:\:\frac{\mathrm{1}}{{S}^{\:\mathrm{30}} }=\left(\mathrm{150}\right)^{\mathrm{3}} \\ $$$$\frac{\mathrm{1}}{{S}_{\mathrm{30}} }=\left(\mathrm{3}\right)^{\mathrm{150}} \\ $$$${obviously}\:\:{S}_{\mathrm{30}} =\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{150}} \\ $$
Commented by Dwaipayan Shikari last updated on 26/Jun/21
$${FUN} \\ $$
Commented by MJS_new last updated on 27/Jun/21
$$\mathrm{yes}!!! \\ $$$$\mathrm{similar}\:\mathrm{to} \\ $$$$\mathrm{log}_{\mathrm{15}} \:{x}\:−\mathrm{log}_{\mathrm{25}} \:{y}\:=\mathrm{150} \\ $$$$\mathrm{log}_{\mathrm{30}} \:\frac{{x}}{{y}}\:=? \\ $$$$\mathrm{log}_{\mathrm{15}} \:{x}\:−\mathrm{log}_{\mathrm{25}} \:{y}\:=\mathrm{log}_{\mathrm{15}−\mathrm{25}} \:\left({x}−{y}\right)\:=\mathrm{log}_{−\mathrm{10}} \:\frac{{x}}{{y}} \\ $$$$\Rightarrow\:\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{10}} \:\frac{{y}}{{x}}}=\mathrm{150} \\ $$$$\Rightarrow\:\frac{\mathrm{1}}{\mathrm{log}_{\mathrm{30}} \:\frac{{y}}{{x}}}=\mathrm{3}^{\mathrm{150}} \\ $$$$\Rightarrow\:\mathrm{log}_{\mathrm{30}} \:\frac{{x}}{{y}}\:=\frac{\mathrm{1}}{\mathrm{150}^{\mathrm{3}} } \\ $$$$\mathrm{let}'\mathrm{s}\:\mathrm{invent}\:\mathrm{The}\:\mathrm{New}\:\mathrm{World}\:\mathrm{Mathematics}! \\ $$
Commented by imjagoll last updated on 27/Jun/21
$$\mathrm{hahahaha}..... \\ $$