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.

y = 4.

Step-by-step 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.

Check the picture below

recall your SOH CAH TOA



we have,
the angle,
the hypotenuse,
we want the opposite side

which of those fellows have only that? ahhhh it has to be Ms Sine,
so let's ask her


the opposite side "x", is how tall the tree is

when taking the sine function, make sure your calculator is in Degree mode, since the angle is in degrees