Solve-without-using-calculator-4-x-3-x-1-2-3-x-1-2-2-2x-1-

Question Number 5568 by Rasheed Soomro last updated on 20/May/16

Solve without using calculator

4^{x} - 3^{x + \frac{1}{2}} = 3^{x - \frac{1}{2}} - 2^{2 x - 1}

Answered by Yozzii last updated on 20/May/16

4^{x} + 2^{2 x - 1} = 3^{x} 3^{- 0.5} + 3^{x} \times 3^{0.5}

4^{x} + 4^{x} \times 0.5 = 3^{x} (\frac{1}{\sqrt{3}} + \sqrt{3})

{(\frac{4}{3})}^{x} = (\sqrt{3} + \frac{1}{\sqrt{3}}) \times \frac{2}{3}

x = \frac{l n ((8 / 3 \sqrt{3}))}{l n (4 / 3)}

x = \frac{l n (\frac{4}{3}) + l n \frac{2}{\sqrt{3}}}{l n (4 / 3)}

x = 1 + \frac{0.5 l n \frac{4}{3}}{l n (4 / 3)}

x = 1 + 0.5

x = 1.5

Commented by Rasheed Soomro last updated on 21/May/16

Solution without logarthm .

From above

{(\frac{4}{3})}^{x} = (\sqrt{3} + \frac{1}{\sqrt{3}}) \times \frac{2}{3}

{(\frac{4}{3})}^{x} = (\sqrt{3} + \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}) \times \frac{2}{3}

{(\frac{4}{3})}^{x} = (\sqrt{3} + \frac{\sqrt{3}}{3}) \times \frac{2}{3}

{(\frac{4}{3})}^{x} = (1 + \frac{1}{3}) \times \frac{2 \sqrt{3}}{3}

{(\frac{4}{3})}^{x} = \frac{4}{3} \times \frac{2 \sqrt{3}}{3}

{(\frac{4}{3})}^{x - 1} = \frac{2}{3^{1 - 1 / 2}} = \frac{4^{1 / 2}}{3^{1 / 2}} = {(\frac{4}{3})}^{1 / 2}

x - 1 = \frac{1}{2}

x = 1 + \frac{1}{2} = \frac{3}{2}

Commented by Yozzii last updated on 20/May/16

M a d e a n e r r o r . S o r r y \sqrt{}

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