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Question Number 7500 by Tawakalitu. last updated on 31/Aug/16

5^(√(x )) − 5^(x − 7) = 100 Find the value of x. x = 9 please workings.

$$\mathrm{5}^{\sqrt{{x}\:}} \:−\:\:\mathrm{5}^{{x}\:−\:\mathrm{7}} \:\:=\:\:\mathrm{100} \\ $$$$ \\ $$$${Find}\:{the}\:{value}\:{of}\:{x}. \\ $$$${x}\:=\:\mathrm{9}\:\:\:{please}\:{workings}. \\ $$

Answered by sandy_suhendra last updated on 01/Sep/16

is this true? 5^(√x) − 5^(x−7) = 100 5^(√x) − 5^(x−7) = 125 − 25 5^(√x) − 5^(x−7) = 5^3 − 5^2 so 5^(√x) = 5^3 or 5^(x−7) = 5^2 (√x) = 3 x−7 = 2 x = 9 x = 9

$${is}\:{this}\:{true}? \\ $$$$\mathrm{5}^{\sqrt{{x}}} \:−\:\mathrm{5}^{{x}−\mathrm{7}} \:=\:\mathrm{100} \\ $$$$\mathrm{5}^{\sqrt{{x}}} \:−\:\mathrm{5}^{{x}−\mathrm{7}} \:=\:\mathrm{125}\:−\:\mathrm{25} \\ $$$$\mathrm{5}^{\sqrt{{x}}} \:−\:\mathrm{5}^{{x}−\mathrm{7}} \:=\:\mathrm{5}^{\mathrm{3}} \:−\:\mathrm{5}^{\mathrm{2}} \\ $$$${so}\:\:\:\mathrm{5}^{\sqrt{{x}}} \:=\:\mathrm{5}^{\mathrm{3}} \:\:\:{or}\:\:\:\mathrm{5}^{{x}−\mathrm{7}} \:=\:\mathrm{5}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\sqrt{{x}}\:=\:\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:{x}−\mathrm{7}\:=\:\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{x}\:=\:\mathrm{9}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}\:=\:\mathrm{9} \\ $$

Commented by Yozzia last updated on 01/Sep/16

Commented by Yozzia last updated on 01/Sep/16

There are two solutions.

$${There}\:{are}\:{two}\:{solutions}.\: \\ $$

Commented by Tawakalitu. last updated on 01/Sep/16

Thanks so much

$${Thanks}\:{so}\:{much} \\ $$

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