Question

Find the value of y in 9^y = 3^5 * 9^6 / 27^3. Please explain the steps which you took in order to answer this question.

Answer 1

y = 4.

Explanation:

We can do this by changing all the base numbers to 3.

Note that 9 = 3^2 and 27 = 3^3.

So the equation becomes:

(3^2)^y = 3^5 * (3^2)^6 / (3^3)^3

By the law of indices:

3^2y = 3^5 * 3^12 / 3^9

3^2y = 3^17/ 3^9

3^2y = 3^8

So since the base is 3 in both terms

2y = 8

y = 4.