Question 55488
Solve the equation 
{{{4^(2x+1)=2^(3x+6)}}}  4 is 2^2 so...
{{{(2^2)^(2x+1)=2^(3x+6)}}}
{{{(2)^(2(2x+1))=2^(3x+6)}}}  Since the bases are equal their exponents are equal:
{{{2(2x+1)=(3x+6)}}}
{{{4x+2=3x+6}}}
{{{-3x+4x+2=-3x+3x+6}}}
{{{x+2=6}}}
{{{x+2-2=6-2}}}
{{{highlight(x=4)}}}
Check by substitution:
{{{4^(2(4)+1)=2^(3(4)+6)}}}
{{{4^(8+1)=2^(12+6)}}}
{{{4^9=2^18}}}
{{{262144=262144}}} We're right!!!
Happy Calculating!!!