Question #9cda7

1 Answer
Oct 13, 2016

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