Evaluate: log_(25)125 Answer:

Determine Power of 25: To evaluate log_(25)125, we need to determine what power we must raise 25 to in order to get 125. We can express 125 as a power of 5, since 125 is 5^3. Similarly, 25 is 5^2. So, we can rewrite the expression as log_(5^2)(5^3).Express Numbers as Powers: Using the property of logarithms that log_(a^m)(b^n) = n/m * log_a(b), we can simplify the expression. In this case, log_(5^2)(5^3) = 3/2 * log_5(5).Simplify Using Logarithm Property: We know that log_5(5) is 1, because 5 raised to the power of 1 is 5. So, 3/2 * log_5(5) = 3/2 * 1.Calculate Logarithm Value: Multiplying 3/2 by 1 gives us 3/2. Therefore, log_(25)125 = 3/2.

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Math Problems

Grade 6

Solve one-step multiplication and division equations with whole numbers

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Q. Evaluate:

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\log _{25} 125

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Answer:

Determine Power of $25$ : To evaluate $\log_{25}125$ , we need to determine what power we must raise $25$ to in order to get $125$ . We can express $125$ as a power of $5$ , since $125$ is $5^3$ . Similarly, $25$ is $5^2$ . So, we can rewrite the expression as $\log_{5^2}(5^3)$ .
Express Numbers as Powers: Using the property of logarithms that $\log_{a^m}(b^n) = \frac{n}{m} \cdot \log_a(b)$ , we can simplify the expression. $\newline$ In this case, $\log_{5^2}(5^3) = \frac{3}{2} \cdot \log_5(5)$ .
Simplify Using Logarithm Property: We know that $\log_5(5)$ is $1$ , because $5$ raised to the power of $1$ is $5$ . So, $\frac{3}{2} \times \log_5(5) = \frac{3}{2} \times 1$ .
Calculate Logarithm Value: Multiplying $\frac{3}{2}$ by $1$ gives us $\frac{3}{2}$ . $\newline$ Therefore, $\log_{25}125 = \frac{3}{2}$ .