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

Find the value of y such that 9^y = 3^5 * 9^6 - id935962714314833, rebelfighter24ovin5h

Ответ:

brobles9118

12.09.2021

Mathematics

${9}^{y} = \frac{ {3}^{5} \times {9}^{6} }{ {27}^{3} } \\$

• express in terms of 3:

${3}^{2y} = \frac{ {3}^{5} \times {3}^{12} }{ {3}^{9} } \\$

• from law of indices:

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

• 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:

$2y = 8 \\ y = \frac{8}{2 } \\ \\ { \underline{ \underline{ \: \: y = 4 \: \: }}}$

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Ответ:

ayoismeisjjjjuan

12.09.2021

Mathematics

Step-by-step explanation:

$9^y=\dfrac{3^5*9^6}{27^3} \\\\\\(3^2)^y=\dfrac{3^5*(3^2)^6}{(3^3)^3} \\\\\\3^{2y}=3^{5+12-9}\\\\\\2y=8\\\\\\y=4\\$

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Ответ:

charlesiarenee0

27.01.2023

Mathematics

15 and 18

Step-by-step explanation:

Create a system of equations. Let x and y represent the numbers:

y = x + 3

x + y = 33

Solve by substitution, by plugging in the first equation into the second equation as y:

x + y = 33

x + (x + 3) = 33

2x + 3 = 33

2x = 30

x = 15

Find the other number by plugging in 15 as x into the first equation:

y = x + 3

y = 15 + 3

y = 18

So, the numbers are 15 and 18

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

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