Question

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

Answer 1

${\huge{\underline{\boxed{\red{\mathcal{Answer}}}}}}$

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!

Answer 2

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

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

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

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

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

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

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

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