solving math problem?

Question

9^ -x = 1/3

please help, explain, trying to get the main idea here, thanks!

Answer 1

9^-x = 1/3 ----> 9^-x = 3^-1

9^-x = 3^-x * 3^-x

3^-x * 3^-x = 3^-2x

3^-2x = 3^-1

Because both bases are 3, we can solve for x by stating -2x = -1

If we solve for X, we get x = 1/2

Answer 2

I assume you mean 9²

9² - x = 1/3

81 - x = 1/3

Clear the fraction. Multiply both sides of the equation by 3

3(81) - 3(x) = 3(1/3)

243 - 3x = 1

Transpose 243

243 - 3x - 243 = 1 - 243

- 3x = - 242

Divide both sides of the equation by - 3

- 3x / - 3 = - 242 / - 3

x = - 242 / - 3

x = 242 / 3

x = 80.6666666666. . .

x = 80.7 Rounded to two decimal places

- - - - - - -s-

Answer 3

By 9^-x I understand 9^(-x), so we have

1/9^x = 1/ 3

9^x = 3, then x Log 9 = Log 3 and

x = Log 3 / Log 9 = Log 3 / Log 3^2 = Log 3 / (2* Log 3) = 1/2

Answer 4

well to understand this
first you have to understand that x^-1=1/x
and x^-2= 1/x^2
so the problem becomes
1/(9^x)=1/3
9^x=3
LOG(9)/LOG(3)=2
x=2

Answer 5

9^-x=1/3
or 3^-2x=3^-1
or -2x=-1
or x=1/2 ans

Answer 6

9^(2)-x=(1)/(3)

81-x=(1)/(3)

-x=-81+(1)/(3)

-x=-(242)/(3)

-x*-1=-(242)/(3)*-1

x=-(242)/(3)*-1

x=(242)/(3)