If 5^(y-4) = 25 and 3^(2x-1)= 27, what is the value of x / y ?

Question

1.) 2/3

2.) 6

3.) 1/6

4.) 1/9

Answer 1

You can solve each of these equations individually. The first can be solved for y, and the second can be solved for x. Since, y and x are in the exponents, you can either solve these using logarithms or by writing both sides of the equations as exponents with the same base.

5^(y-4) = 25

5^2 = 25, so

5^(y-4) = 5^2

Now that both sides of the equation have the same base, we can set their exponents equal to each other.

y - 4 = 2

y = 6

And we can take the same approach with the other equation.

3^(2x-1) = 27

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

2x - 1 = 3

2x = 4

x = 2

If y = 6 and x = 2, then x/y = 2/6 = 1/3