Question 841736
A rule about exponents:  {{{b^(a+c)=(b^a)*(b^c)}}}.


See that in your equation you have a term {{{2^(x+1)}}}, and you can do this:
{{{2^(x+1)=(2^(x-1))(2^2)}}}.


Some steps........
{{{(2^(x+1))=(2^(x-1))+48}}}
{{{2^(x+1)-2^(x-1)=48}}}
{{{(2^(x-1))(2^2-1)=48}}}
{{{(2^(x-1))(4-1)=48}}}
{{{(2^(x-1))*3=48}}}  and then factor 48
{{{3*2^(x-1)=3*2^4}}}
{{{2^(x-1)=2^4}}}, the bases are the same, so the exponents must be equal.
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{{{x-1=4}}}
{{{x=4+1}}}
{{{highlight(x=5)}}}