Find n. 9^(n)+9^(n)+9^(n)=3^(99)

Combine like terms: Combine like terms on the left side of the equation. Since we have three terms of 9^(n), we can add them together. 9^(n) + 9^(n) + 9^(n) = 3 * 9^(n)Rewrite using combined term: Rewrite the equation using the combined term. 3 * 9^(n) = 3^(99)Express 9 as power of 3: Express 9 as a power of 3 because 9 is 3 squared (3^2). 9^(n) = (3^2)^(n)Apply power of power rule: Apply the power of a power rule to simplify the left side of the equation. (3^2)^(n) = 3^(2n) So, 3 * 3^(2n) = 3^(99)Factor out common base: Factor out the common base of 3 on the left side of the equation. 3^(1) * 3^(2n) = 3^(99)Apply product of powers rule: Apply the product of powers rule to combine the exponents on the left side. 3^(1+2n) = 3^(99)Set exponents equal: Set the exponents equal to each other because the bases are the same. 1 + 2n = 99Solve for n: Solve for n by subtracting 1 from both sides of the equation. 2n = 99 - 1 2n = 98Divide by 2: Divide both sides by 2 to solve for n. n = 98 / 2 n = 49

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Find $n$ . $\newline$ $9^{n}+9^{n}+9^{n}=3^{99}$

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Algebra 2

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Q. Find

n

\newline

9^{n}+9^{n}+9^{n}=3^{99}

Combine like terms: Combine like terms on the left side of the equation. $\newline$ Since we have three terms of $9^{n}$ , we can add them together. $\newline$ $9^{n} + 9^{n} + 9^{n} = 3 \times 9^{n}$
Rewrite using combined term: Rewrite the equation using the combined term. $3 \times 9^{n} = 3^{99}$
Express $9$ as power of $3$ : Express $9$ as a power of $3$ because $9$ is $3$ squared ( $3^2$ ). $\newline$ $9^{n} = (3^2)^{n}$
Apply power of power rule: Apply the power of a power rule to simplify the left side of the equation. $\newline$ $(3^2)^n = 3^{2n}$ $\newline$ So, $3 \times 3^{2n} = 3^{99}$
Factor out common base: Factor out the common base of $3$ on the left side of the equation. $\newline$ $3^{1} \times 3^{2n} = 3^{99}$
Apply product of powers rule: Apply the product of powers rule to combine the exponents on the left side. $\newline$ $3^{1+2n} = 3^{99}$
Set exponents equal: Set the exponents equal to each other because the bases are the same. $1 + 2n = 99$
Solve for n: Solve for n by subtracting $1$ from both sides of the equation. $\newline$ $2n = 99 - 1$ $\newline$ $2n = 98$
Divide by $2$ : Divide both sides by $2$ to solve for $n$ . $n = \frac{98}{2}$ $n = 49$