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Question Number 8635 by tawakalitu last updated on 19/Oct/16

Find the value of x 5^(√x) − 5^x − 7 = 100

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

Answered by ridwan balatif last updated on 19/Oct/16

5^(√x) −5^x =107 x≥0 it′s impossible if 5^(√x) −5^x have a positive value,so there is no value of x example: if x=0→5^(√0) −5^0 =0→0≠107 x=4→5^(√4) −5^4 =−600→−600≠107 x=(1/2)→5^(1/4) −5^(1/2) ≈−0.740→−0.740≠107

$$\mathrm{5}^{\sqrt{\mathrm{x}}} −\mathrm{5}^{\mathrm{x}} =\mathrm{107} \\ $$$$\mathrm{x}\geqslant\mathrm{0} \\ $$$$\mathrm{it}'\mathrm{s}\:\mathrm{impossible}\:\mathrm{if}\:\mathrm{5}^{\sqrt{\mathrm{x}}} −\mathrm{5}^{\mathrm{x}} \:\mathrm{have}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{value},\mathrm{so} \\ $$$$\mathrm{there}\:\mathrm{is}\:\mathrm{no}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$$$\mathrm{example}: \\ $$$$\mathrm{if}\:\mathrm{x}=\mathrm{0}\rightarrow\mathrm{5}^{\sqrt{\mathrm{0}}} −\mathrm{5}^{\mathrm{0}} =\mathrm{0}\rightarrow\mathrm{0}\neq\mathrm{107} \\ $$$$\:\:\:\:\mathrm{x}=\mathrm{4}\rightarrow\mathrm{5}^{\sqrt{\mathrm{4}}} −\mathrm{5}^{\mathrm{4}} =−\mathrm{600}\rightarrow−\mathrm{600}\neq\mathrm{107} \\ $$$$\:\:\:\:\mathrm{x}=\frac{\mathrm{1}}{\mathrm{2}}\rightarrow\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{4}}} −\mathrm{5}^{\frac{\mathrm{1}}{\mathrm{2}}} \approx−\mathrm{0}.\mathrm{740}\rightarrow−\mathrm{0}.\mathrm{740}\neq\mathrm{107} \\ $$

Commented by tawakalitu last updated on 19/Oct/16

Thank you sir.

$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{sir}. \\ $$

Commented by ridwan balatif last updated on 19/Oct/16

your welcome

$$\mathrm{your}\:\mathrm{welcome}\: \\ $$

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