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1 vote
Find the value of y such that 9^y = 3^5 * 9^6 / 27^3. Explain how you solved this problem.

2 Answers

7 votes

Answer:

Explanation:


9^y=(3^5*9^6)/(27^3) \\\\\\(3^2)^y=(3^5*(3^2)^6)/((3^3)^3) \\\\\\3^(2y)=3^(5+12-9)\\\\\\2y=8\\\\\\y=4\\

User Lekso
by
4.2k points
4 votes

Answer:


{9}^(y) = \frac{ {3}^(5) * {9}^(6) }{ {27}^(3) } \\

• express in terms of 3:


{3}^(2y) = \frac{ {3}^(5) * {3}^(12) }{ {3}^(9) } \\

• from law of indices:


{a}^(n) * {a}^(m) = {a}^((n + m)) \\ \\ \frac{ {a}^(n) }{ {a}^(m) } = {a}^((n - m))

• therefore, let's apply the laws:


{3}^(2y) = {3}^((5 + 12 - 9)) \\ \\ {3}^(2y) = {3}^(8)

• from third law of indices:


\{ {a}^(x) = {a}^(y) \} \equiv \{x = y \}

• apply the law:


2y = 8 \\ y = (8)/(2 ) \\ \\ { \underline{ \underline{ \: \: y = 4 \: \: }}}

User Lowkase
by
4.5k points