Math, asked by hareem23, 3 months ago

Solve 2 to power x+1 + 2 to power x+ 2 =192​

Answers

Answered by MrImpeccable
23

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Given:

  •  2^{x+1} + 2^{x+2} = 192

To Find:

  • Value of x

Solution:

 \longrightarrow 2^{x+1} + 2^{x+2} = 192 \\:\implies 2^{x+1} + 2^{x+1}*2 = 192 \\:\implies</p><p>2^{x+1}(1 + 2) = 192 \\:\implies 2^{x+1} = 64 \\:\implies 2^x * 2 = 64 \\:\implies 2^x = 32 \\:\implies 2^x = 2^5 \\\bf{:\implies x = 5}

hope it helps!

Answered by Heer56
2

\sf \color{purple} {2}^{x + 1}   +  {2}^{x + 2}  = 192

 \sf \color{blue}( {2}^{x} )(  {2}^{x}  ) + ( {2}^{x} )( {2}^{2} ) = 192

 \sf \color{red}( {2}^{x})( {2}^{2} )  + ( {2}^{x} )(2 \times 2 = 4) = 192

 \sf \color{navy}(4 + 2) + ( {2}^{x}  +  {2}^{x} )

 \sf \color{indigo}(6 )(  {2}^{x} ) = 192

 \sf \color{green}( {2}^{x} ) =  \cancel  \frac {192}{6}

 \sf \color{orange} {2}^{x}  = 32

 \sf \therefore \red{x = 5} .. \: .. \: ..   \:  \:  \:  \:  \:  \: ( \therefore {2}^{5}  = 32)

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