Identify Base and Number: Identify the base of the logarithm and the number whose logarithm is to be found. The base is 5, and the number is 3125.Check Power of 5: Determine if 3125 can be expressed as a power of 5. 3125 is 5 raised to some power because 5 is a prime number and 3125 is a multiple of 5.Find Power of 5: Find the power to which 5 must be raised to get 3125. By trial, 5^5 = 3125.Write as Power of 5: Write 3125 as a power of 5 in the logarithmic expression. log_(5)3125 becomes log_(5)(5^5).Apply Power Property: Apply the power property of logarithms. The power property states that log_b(a^n) = n * log_b(a). Therefore, log_(5)(5^5) becomes 5 * log_(5)5.Evaluate Logarithm: Evaluate log_(5)5. The logarithm of a number to the same base is 1. So, log_(5)5 is 1.Multiply Exponent: Multiply the exponent by the logarithm of the base to the same base. 5 * log_(5)5 becomes 5 * 1.Calculate Final Result: Calculate the final result. 5 * 1 equals 5.

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$\log _{5} 3125=$

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Algebra 2

Evaluate logarithms using properties

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\log _{5} 3125=

Identify Base and Number: Identify the base of the logarithm and the number whose logarithm is to be found. $\newline$ The base is $5$ , and the number is $3125$ .
Check Power of $5$ : Determine if $3125$ can be expressed as a power of $5$ . $3125$ is $5$ raised to some power because $5$ is a prime number and $3125$ is a multiple of $5$ .
Find Power of $5$ : Find the power to which $5$ must be raised to get $3125$ . By trial, $5^5 = 3125$ .
Write as Power of $5$ : Write $3125$ as a power of $5$ in the logarithmic expression. $\newline$ $\log_{5}3125$ becomes $\log_{5}(5^5)$ .
Apply Power Property: Apply the power property of logarithms. $\newline$ The power property states that $\log_b(a^n) = n \cdot \log_b(a)$ . $\newline$ Therefore, $\log_{5}(5^5)$ becomes $5 \cdot \log_{5}5$ .
Evaluate Logarithm: Evaluate $\log_{5}5$ . The logarithm of a number to the same base is $1$ . So, $\log_{5}5$ is $1$ .
Multiply Exponent: Multiply the exponent by the logarithm of the base to the same base. $5 \times \log_{5}5$ becomes $5 \times 1$ .
Calculate Final Result: Calculate the final result. $\newline$ $5 \times 1$ equals $5$ .