maths question (1 Viewer)

[meg_1_2_3_4_5]

3^t x 9^(t+1) = 1/3

seems like an easy question, but me and the solutions have conflicting answers. The way i tried to work it out is by making the base the same:
3^t x 3^ (2t +2) = 3^-1
and therefore:
t(2t +2) +1 = 0 (a quadratic equation with no solutions)

the answers stuff up (i think) cos they end up with x= -1, but that is only with a plus between the first 2 terms of the original equation, which would mean a linear equation (x +2x +2 = -1) that is simple to solve.
any help would be appreciated

 

[webby234]

3^t x 3^{2t + 2} = 1/3

1/3 = 3^{3t + 2}
3t + 2 = 1
3t = -3
t = -1

Remember that when you multiply x^m by xⁿ you get x^{m + n} not x^mn

 

[SoulSearcher]

a^x * a^y = a^x+y
Therefore
3^t * 9^t+1
= 3^t * 3^2t+1
= 3^3t+2

From there, you can solve it

EDIT: webby beat me to it

 

[meg_1_2_3_4_5]

true true
just had a bit of a blonde moment i think