Mathematic Problems

210. példa

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

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

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

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

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

3^{\frac{x - 3}{2}} \cdot 3^{\frac{2}{2}} - 3^{\frac{x - 3}{2}} = 2^{\frac{x - 2}{3}} + 2^{\frac{x - 2}{3}} \cdot 2^{\frac{3}{3}}

3^{\frac{x - 3}{2}} \cdot 3 - 3^{\frac{x - 3}{2}} = 2^{\frac{x - 2}{3}} + 2^{\frac{x - 2}{3}} \cdot 2

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

3^{\frac{x - 3}{2}} \cdot 2 = 2^{\frac{x - 2}{3}} \cdot 3

\frac{3^{\frac{x - 3}{2}}}{3} = \frac{2^{\frac{x - 2}{3}}}{2}

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

3^{\frac{x - 3 - 2}{2}} = 2^{\frac{x - 2 - 3}{3}}

3^{\frac{x - 5}{2}} = 2^{\frac{x - 5}{3}}

{(3^{\frac{1}{2}})}^{x - 5} = {(2^{\frac{1}{3}})}^{x - 5}

{(\sqrt{3})}^{x - 5} = {(\sqrt[3]{2})}^{x - 5}

\frac{{(\sqrt{3})}^{x - 5}}{{(\sqrt[3]{2})}^{x - 5}} = 1

{(\frac{\sqrt{3}}{\sqrt[3]{2}})}^{x - 5} = 1

x - 5 = 0

x = 5

x = 5

Matematika - Képlettár