If (27^(x))/(9^(y))=81, what is the value of 3x-2y ?

Express in Prime Factors: We are given the equation (27^(x))/(9^(y))=81. We need to find the value of 3x-2y. First, we express 27 and 9 in terms of their prime factor, which is 3. 27 = 3^3 and 9 = 3^2.Rewrite Using Prime Factors: Now we rewrite the given equation using these expressions: (3^3)^x / (3^2)^y = 81 This simplifies to: 3^(3x) / 3^(2y) = 81Express 81 as Power of 3: Since 81 is also a power of 3, we express 81 as 3^4. So the equation becomes: 3^(3x) / 3^(2y) = 3^4Combine Left Side of Equation: Using the property of exponents that a^(m)/a^(n) = a^(m-n), we can combine the left side of the equation: 3^(3x - 2y) = 3^4Set Exponents Equal: Since the bases are the same and the equation is an equality, the exponents must be equal. Therefore, we can set the exponents equal to each other: 3x - 2y = 4Find Value of 3x - 2y: We have found the value of 3x - 2y, which is 4.

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If
(27^(x))/(9^(y))=81, what is the value of
3x-2y ?

If $\frac{27^{x}}{9^{y}}=81$ , what is the value of $3 x-2 y$ ?

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Algebra 2

Composition of linear and quadratic functions: find a value

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Q. If

\frac{27^{x}}{9^{y}}=81

, what is the value of

3 x-2 y

Express in Prime Factors: We are given the equation $\frac{27^{x}}{9^{y}}=81$ . We need to find the value of $3x-2y$ . First, we express $27$ and $9$ in terms of their prime factor, which is $3$ . $27 = 3^{3}$ and $9 = 3^{2}$ .
Rewrite Using Prime Factors: Now we rewrite the given equation using these expressions: $\newline$ $\frac{(3^3)^x}{(3^2)^y} = 81$ $\newline$ This simplifies to: $\newline$ $\frac{3^{3x}}{3^{2y}} = 81$
Express $81$ as Power of $3$ : Since $81$ is also a power of $3$ , we express $81$ as $3^4$ . $\newline$ So the equation becomes: $\newline$ $\frac{3^{3x}}{3^{2y}} = 3^4$
Combine Left Side of Equation: Using the property of exponents that $\frac{a^{m}}{a^{n}} = a^{m-n}$ , we can combine the left side of the equation: $\newline$ $3^{3x - 2y} = 3^{4}$
Set Exponents Equal: Since the bases are the same and the equation is an equality, the exponents must be equal. Therefore, we can set the exponents equal to each other: $3x - 2y = 4$
Find the Value of $3x - 2y$ : We have found the value of $3x - 2y$ , which is $4$ .