Question

Question #9cda7

Answer 1

`y = 3x-1`

Explanation:

We will use the following properties of exponents and of logarithms:

• `a^(-x) = 1/a^x`
• `(a^x)^y = a^(xy)`
• `a^x*a^y = a^(x+y)`
• `log_a(a^x) = x`

With those

`3^y/27^x=1/3`

`=> 3^y/(3^3)^x = 3^(-1)`

`=> 3^y/3^(3x) = 3^(-1)`

`=> 3^y = 3^(3x)*3^(-1)`

`=> 3^y = 3^(3x-1)`

`=> log_3(3^y) = log_3(3^(3x-1))`

`:. y = 3x-1`