Question

solve for x: 8^x+1=16^x+2​

Answer 1

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Solve for x : 8^x+1=16^x+2

$\mathtt{\huge{\underline{\red{Answer\: :}}}}$

$\: \large \green{ \bold{ \underline{step \: by \: step \: explaination : }}}$

$\: \implies \displaystyle \sf \: {8}^{x + 1} = {16}^{x + 2}$

$\: \implies \displaystyle \sf \: {2}^{3(x + 1)} = {2}^{4(x + 2)}$

$\: \implies \displaystyle \sf \: 3( x + 1) = 4( x + 2)$

$\: \implies \displaystyle \sf3x + 3 = 4x + 8$

$\: \implies \displaystyle \sf \: 3x + 3 - 4x - 8 = 0$

$\: \implies \displaystyle \sf \: - x + 11 = 0$

$\: \: \implies \displaystyle \sf{x = 11}$

$\: \boxed{ \boxed{ \underline{ \underline{ \bf{the \: answer \: will \: be \: x = 11}}}}}$