સમીકરણ {4^x} - {3^{x,; - ;frac{1}{2}}} = {3^{ | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

${4^x} - {3^{x - \frac{1}{2}}} = {3^{x + \frac{1}{2}}} - {2^{2x - 1}}$ સમીકરણ આપેલ છે.

$ \Rightarrow \,\,{2^{2x}} + {2^{2x - 1}} = {3^{x + \frac{1}

Vedclass · Accepted Answer

$\frac{3}{2}$

Vedclass · Answer

${4^x} - {3^{x - \frac{1}{2}}} = {3^{x + \frac{1}{2}}} - {2^{2x - 1}}$ સમીકરણ આપેલ છે.

$ \Rightarrow \,\,{2^{2x}} + {2^{2x - 1}} = {3^{x + \frac{1}{2}}} + {3^{x - \frac{1}{2}}}$

$ \Rightarrow \,\,{2^{2x}}\left( {1 + \frac{1}{2}} ight) = {3^{x - \frac{1}{2}}}(1 + 3)$

$ \Rightarrow \,{2^{2x}}.\frac{3}{2} = {3^{x - \frac{1}{2}}}.4$

$ \Rightarrow \,{2^{2x - 3}} = {3^{x - \frac{3}{2}}}$

હવે  બંને બાજુ ${m{log }}$ લેતાં $,  \Rightarrow {m{ }}\,(2x - 3)\log 2 = (x - 3/2)\log 3$

$ \Rightarrow \,2x\log 2 - 3\log 2 = x\log 3 - \frac{3}{2}\log 3$

$ \Rightarrow x\log 4 - x\log 3 = 3\log 2 - \frac{3}{2}\log 3$

$ \Rightarrow \,x\log \left( {\frac{4}{3}} ight) = \log 8 - \log 3\sqrt 3 $

$ \Rightarrow \,{\left( {\frac{4}{3}} ight)^x} = \frac{8}{{3\sqrt 3 }}$

$ \Rightarrow \,{\left( {\frac{4}{3}} ight)^x} = {\left( {\frac{4}{3}} ight)^{3/2}}$

$	herefore \,\,x = \frac{3}{2}$

સમીકરણ ${4^x} - {3^{x\,\; - \;\frac{1}{2}}} = {3^{x + \frac{1}{2}}} - {2^{2x - 1}}\,$ માં ${\rm{x}}$ કિંમત =.....

Similar Questions

સમીકરણ $\sqrt {x + 3 - 4\sqrt {x - 1} } + \sqrt {x + 8 - 6\sqrt {x - 1} } = 1$ નો ઉકેલ મેળવો

જો $\alpha, \beta$ એ સમીકરણ $x^2-x-1=0$ ના બીજ હોય અને $\mathrm{S}_{\mathrm{n}}=2023 \alpha^{\mathrm{n}}+2024 \beta^{\mathrm{n}}$ હોય, તો :

જો ${\rm{x}}$ બરાબર શું થાય, તો $\frac{{8{x^2}\, + \,16x\, - \,51}}{{(2x - \,3)\,(x\, + \,4)}}\, > \,3\,\, = \,\,\,......$