Question 565424
Solve for x: 

{{{7^(x+2)-7^x=48*sqrt( 7 )}}}
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We can factor the expression as follows:
{{{7^x*(7^2-1)=48*sqrt(7)}}}
{{{7^x*(48) = 48*sqrt(7)}}}

{{{7^x = sqrt(7) = 7^(1/2)}}}
From here, we can read off the answer x = 1/2, or solve using logarithms:
{{{x*log(7) = (1/2)*log(7)}}}
Dividing through be log(7) gives x = 1/2