if 3^a=5√3^4 , what is the value of a ?

Simplify right side: Simplify the right side of the equation. We need to simplify 5√3^4. The square root of 3^4 is 3^2 because (3^2)^2 = 3^4. So, 5√3^4 = 5 * 3^2.Continue simplifying: Continue simplifying the right side of the equation. Now we calculate 5 * 3^2. Since 3^2 = 9, we have 5 * 9 = 45. So, 5√3^4 = 45.Rewrite equation: Rewrite the equation with the simplified right side. Now we have 3^a = 45.Express as power: Express 45 as a power of 3, if possible. We need to express 45 as a power of 3 to compare the exponents. However, 45 is not a power of 3, so we cannot directly compare exponents.Find prime factorization: Find the prime factorization of 45. The prime factorization of 45 is 3 * 3 * 5, which is 3^2 * 5.Compare factorization: Compare the prime factorization of 45 with 3^a. We have 3^a = 3^2 * 5. Since there is an extra factor of 5 on the right side, we cannot find an integer value for a that will satisfy the equation.

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if $3^a=5\sqrt{3^4}$ , what is the value of $a$ ?

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Algebra 2

Solve exponential equations by rewriting the base

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Q. if

3^a=5\sqrt{3^4}

, what is the value of

a

Simplify right side: Simplify the right side of the equation. $\newline$ We need to simplify $5\sqrt{3^4}$ . The square root of $3^4$ is $3^2$ because $(3^2)^2 = 3^4$ . $\newline$ So, $5\sqrt{3^4} = 5 \times 3^2$ .
Continue simplifying: Continue simplifying the right side of the equation. $\newline$ Now we calculate $5 \times 3^2$ . Since $3^2 = 9$ , we have $5 \times 9 = 45$ . $\newline$ So, $5\sqrt{3^4} = 45$ .
Rewrite equation: Rewrite the equation with the simplified right side. $\newline$ Now we have $3^a = 45$ .
Express as power: Express $45$ as a power of $3$ , if possible. $\newline$ We need to express $45$ as a power of $3$ to compare the exponents. However, $45$ is not a power of $3$ , so we cannot directly compare exponents.
Find prime factorization: Find the prime factorization of $45$ . The prime factorization of $45$ is $3 \times 3 \times 5$ , which is $3^2 \times 5$ .
Compare factorization: Compare the prime factorization of $45$ with $3^a$ . We have $3^a = 3^2 \times 5$ . Since there is an extra factor of $5$ on the right side, we cannot find an integer value for $a$ that will satisfy the equation.