Question

Solve for x
(3x)^6=3^-6

Answer 1

We can take the cube root of both sides to get
(3x)^2 = 3^(-2)
Now we can "take the square root", but must keep in mind that there is a positive and a negative answer, so that
\[3x = \pm(3^{-1}) = \pm{1 \over 3}\]and hence
\[x = \pm{1 \over 9}\]I'm assuming x is only allowed to be real. There are four additional complex solutions to this (which would come out at the point that I took the cube root), but I won't bother typing it out unless you want/need to know what they are.

Answer 2

the answer is 1/9 ?

Answer 3

Write both sides with the exponent of 6

Answer 4

positive or negative 1/9
Because a negative to an even power is positive.

Answer 5

\[(3x)^6=(\frac{1}{3})^6\]

Answer 6

no it (3^x)^6=3^-6

Answer 7

Since the expressions are equal and the exponents are the same, the bases must also be the same so write:
\[3x=\frac{1}{3}\]

Answer 8

Solve that.

Answer 9

\[(3^x)^6=3^{6x}\]

Answer 10

So:
\[3^{6x}=3^{-6}\]

Answer 11

So 6x=-6

Answer 12

x=-1

Answer 13

thank you !!!!!!!!!!!!!!!!!!!!

Answer 14

yw