Solve for X?

Question

27^(2x) = 9^(x-3)

I do not know how to solve for x with these types of exponets, so any help with be much appreciated.

Answer 1

27^(2x) = 9^(x-3)
(2x)ln[27]=(x-3)ln[9]
(2x)/(x-3)=ln[9]/ln[27]
(2x)/(x-3)=2/3
6x=2x-6
6x-2x=-6
4x=-6
x=-3/2

Answer 2

27^(2x) = 9^(x-3)

Using logarithms, we add the symbol [ log ] to each sides,
[ We are using log 3 in this case since 9 and 27 is divisible by 3]
log 27^(2x) = log 9^(x - 3)

Recall that the law of logarithms states that log a^b = b log a
Therefore,
2x log 27 = (x - 3) log 9
2x / x - 3 = log 9 / log 27
2x / (x - 3) = log 3^2 / log 3^3 [9 = 3^2 ; 27 = 3^3]
2x / (x - 3) = 2 log 3 / 3 log 3 [ log 3 3 = 1]
2x / (x - 3) = 2/3
Cross multiply,
6x = 2x - 6
4x = -6
x = -6/4
x = -3/2 or -1.5

Answer 3

27=3^3
9=3^2
so
27^(2x) = 9^(x-3)<=>
3^(6x) = 3^ (2x-6)<=>
6x=2x-6<=>
4x=-6<=>
x=-3/2

Answer 4

27^(2x) = 9^(x-3)

3^3(2x) = 3^2(x-3) =3(2x) = 2(x-3) =6x =2x-6 = 6x-2x =-6
4x =-6, x =-6/4 , x=-3/2

Answer 5

1- get the #'s the same (9 &27) so multiply 9 by 3.
2-doing this makes (x-3) multiplied by 3.
3-get rid of the 27s, you dont need them, so the equation is 2x=3(x-3)
4-distribute 2x=3x-9
5- move 3x -x=-9
6 take out negative x=9.

Answer 6

27^(2x) = 9^(x-3)
(3^3)^(2x) = (3^2)^(x-3)
3^(6x) = 3^(2x-6)

6x = 2x - 6
4x = -6
x = -6/4 = -3/2

Answer 7

27^(2x) = 9^(x-3)
(3^3)^(2x) = (3^2)^(x-3)
3^(6x) = 3^(2x-6)
6x = 2x-6
4x = - 6
x = -1.5

Answer 8

27^(2x) = (3^3)^(2x) = 3^(6x) ......(a)
9^(x-3) = (3^2)^(x-3) = 3^(2x-6) .......(b)
(a) = (b)
6x = 2x - 6
6x - 2x = -6
4x = -6
x = -(6/4) = -1.5

Answer 9

(3^3)^(2x) = (3^2)^(x - 3)
3^(6x) = 3^(2)(x - 3)
6x = 2x - 6
4x = - 6
x = - 3 / 2