Asked by cain

solve the exponential equation.
4^(x+2)=9x
Answered by Reiny
A rough sketch of
y = 4^(x+2) and y = 9x shows that the two can never meet.
So, there is no solution

Did you mean:
4^(x+2) = 9^x ?
Answered by cain
yes i meant 4^(x+2)=9^x
Answered by Reiny
ok, then take log of both sides

log (4^(x+2) ) = log (9^x)
(x+2)log4 = xlog9
xlog4 + 2log4= xlog9
2log4 = xlog9 - xlog4
x(log9-log4) = 2log4
x = 2log4/(log9-log4)
button-pushing time ....
x = appr 3.419
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