Question

If 8^x+1=64 what is the value of 2^x+1

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{2^{x+1}=4}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies {8}^{x + 1} = 64 \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies {2}^{x + 1} =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {8}^{x + 1} = 64 \\ \\ \tt: \implies {8}^{x + 1} = {8}^{2} \\ \\ \text{Both \: sides \: bases \: are \: same} \\ \text{So, \: powers \: are \: also \: same} \\ \\ \tt: \implies x + 1 = 2 \\ \\ \tt: \implies x = 2 - 1 \\ \\ \green{\tt: \implies x = 1} \\ \\ \bold{For \: finding \: value :} \\ \tt: \implies {2}^{x + 1} \\ \\ \tt: \implies {2}^{1 + 1} \\ \\ \tt: \implies {2}^{2} \\ \\ \green{\tt: \implies 4} \\ \\ \green{\tt \therefore 2^{x + 1} = 4}$

Answer 2

In the above Question , the following information is given -

$\sf{ 8^ {x + 1 } = 64 }$

We have to find the value of $\sf{ 2^ {x + 1 } }$

SoLuTiOn -

$\sf{ 8^ {x + 1 } = 64 } \\ \\ \sf{8^ {x + 1 } = {8}^{2} } \\ \\ \sf{Hence \: x \: + 1 = 2} \\ \\ \sf{ = > x + 1 = 2} \\ \\ \sf{ = > x+ 1 - 1 = 2- 1} \\ \\ \sf{ \therefore{x = 1}}$

$\sf{Now \: we \: have \: to \: find \: the \: value \: of - } \\ \\ \sf{ {2}^{x + 1} } \\ \\ \sf{We \: found \: earlier \: that \: x \: = 1} \\ \\ \sf{Substituting \: that \: value \: of \: x \: - \: } \\ \\ \sf{ = > {2}^{ 1+ 1} } \\ \\ \sf{ = > {2}^{2} } \\ \\ \sf{ = > 4}$

Hence the required value is 4 .....

__________________