Question

Find the value of y in the equation attached to this question

Answer 1

Answer:

y = 4

Step-by-step explanation:

Decompose  in base 3

$9^{y} =\frac{3^{5} (3^{2})^{6} }{(3^{3})^{3} } =\frac{3^{5}3^{12} }{3^{9} } =\frac{3^{17} }{3^{9} } =3^{17-9} =3^{8}$

if

$3^{8} =(3^{2} )^{4} =9^{4}$

then

$9^{y} =9^{4}$

$y=4$

Hope this helps

Answer 2

Answer:

y = 4

Step-by-step explanation:

1) Simplify $3^5$ to 243.

${9}^{y}=\frac{243\times {9}^{6}}{{27}^{3}}$

2) Simplify ${9}^{6}$ to 531441.

${9}^{y}=\frac{243\times 531441}{{27}^{3}}$

3)  Simplify  $243\times 531441$ to  129140163.

${9}^{y}=\frac{129140163}{{27}^{3}}$

4) Simplify  ${27}^{3}$  to  19683.

${9}^{y}=\frac{129140163}{19683}$

5) Simplify  $\frac{129140163}{19683}$ to 6561.

${9}^{y}=6561$

6) Convert both sides to the same base.

$9^y=9^4$

7)  Cancel the base of 9 on both sides.

$y=4$

Cheers,

ROR