Question

simple exponential equations problem!

determine the exact value of x

3^(2x)= 5(3^x)+ 36

Answer 1

treat it like a quadratic
u = 3^x
_>u^2-5u-36 = 0
Factor and solve for u
Then replace u with 3^x and solve for x

Answer 2

ok so i factored and go (u-9)(u+4).. i dont really understand what to do next!

Answer 3

good solve each part separately
u-9 =0
u+4=0

Answer 4

ok, so u=9 and -4

Answer 5

which means
3^x = 9
and
3^x = -4
Find x

Answer 6

but the left side of the equation is 3^(2x), not 3^x...

Answer 7

correct but took care of that part when we made it a quadratic
3^2x became u^2
dont worry its the same x

Answer 8

ok so for 3^x=9, x = 2

but i dont know how to do it for the other one

Answer 9

good actually the one doesnt exist
3^x > 0

Answer 10

graph it to see for yourself

Answer 11

there is only one answer of 2

Answer 12

ok awesome! thank you sososo much!

Answer 13

welcome