Maths Question (1 Viewer)

[scrubs.]

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<!-- google_ad_section_end -->

 

[Mattamz]

3^t x 9^(t+1) = 1/3
3^t . 3^(2t + 2) = 3^-1
3t + 2 = -1
t = -1

 

[ssglain]

3^t x 3^ (2t +2) = 3^-1
and therefore:
t(2t +2) +1 = 0

That step is wrong. Remember the basic index law: (x^m)*(x^n) = x^(m+n)

 

[PC]

3^t x 9^t+1 = 1/3
3^t x 3^2(t+1) = 3^-1
3^{t + 2(t+1)} = 3^-1
t + 2(t+1) = -1
t + 2t + 2 = -1
3t + 2 = -1
3t = -3
t = -1

 

[loloutaface]

3^t x 9^t+1 = 1/3
3^t x 3^2(t+1) = 3^-1
3^{t + 2(t+1)} = 3^-1
t + 2(t+1) = -1
t + 2t + 2 = -1
3t + 2 = -1
3t = -3
t = -1

i lyk 2 follow PC's explanations coz he explains it thoroughly step by step n he noes how 2 use forum superscripts n subscripts

 

[teambaghdatis]

Here is how you do it guys:
3^t x 9^(t+1) = 1/3
3^t x 3^2(t+1) = 1/3 because 3^2 = 9
3^(3t+2) = 1/3
Now use the log rules
In3^(3t+2) = In(1/3)
(3t+2)In3 = In(1/3)
3t+2 = In(1/3)/In3
3t = (In(1/3)/In3)-2
t = ((In(1/3)/In3)-2)/3
Now sub into calculator
t = -1