We're glad you stopped by Evaluate the expression without using a calculator tex log 5 frac 1 25 tex tex log 5 frac 1 25 tex. This page is here to walk you through essential details with clear and straightforward explanations. Our goal is to make your learning experience easy, enriching, and enjoyable. Start exploring and find the information you need!
Answer :
To evaluate the expression [tex]\(\log_5 \frac{1}{25}\)[/tex], we can use some basic properties of logarithms.
Here is a step-by-step explanation:
1. Recognize the Fraction as a Power:
- The number [tex]\(\frac{1}{25}\)[/tex] can be rewritten as [tex]\(25^{-1}\)[/tex].
- Since [tex]\(25\)[/tex] is the same as [tex]\(5^2\)[/tex], we can express [tex]\(\frac{1}{25}\)[/tex] as [tex]\((5^2)^{-1}\)[/tex].
2. Simplify the Power Expression:
- Using properties of exponents, when you have [tex]\((a^b)^c\)[/tex], it equals [tex]\(a^{b \cdot c}\)[/tex].
- Therefore, [tex]\((5^2)^{-1} = 5^{-2}\)[/tex].
3. Apply the Logarithm Power Rule:
- There is a logarithm property that says [tex]\(\log_b(a^n) = n \cdot \log_b(a)\)[/tex].
- Applying this to [tex]\(\log_5(5^{-2})\)[/tex], we get [tex]\(-2 \cdot \log_5(5)\)[/tex].
4. Evaluate the Base Logarithm:
- By definition, [tex]\(\log_5(5) = 1\)[/tex] because 5 to the power of 1 is 5.
5. Calculate the Final Result:
- Now substitute back: [tex]\(-2 \cdot \log_5(5) = -2 \cdot 1 = -2\)[/tex].
So, the value of [tex]\(\log_5 \frac{1}{25}\)[/tex] is [tex]\(-2\)[/tex].
Here is a step-by-step explanation:
1. Recognize the Fraction as a Power:
- The number [tex]\(\frac{1}{25}\)[/tex] can be rewritten as [tex]\(25^{-1}\)[/tex].
- Since [tex]\(25\)[/tex] is the same as [tex]\(5^2\)[/tex], we can express [tex]\(\frac{1}{25}\)[/tex] as [tex]\((5^2)^{-1}\)[/tex].
2. Simplify the Power Expression:
- Using properties of exponents, when you have [tex]\((a^b)^c\)[/tex], it equals [tex]\(a^{b \cdot c}\)[/tex].
- Therefore, [tex]\((5^2)^{-1} = 5^{-2}\)[/tex].
3. Apply the Logarithm Power Rule:
- There is a logarithm property that says [tex]\(\log_b(a^n) = n \cdot \log_b(a)\)[/tex].
- Applying this to [tex]\(\log_5(5^{-2})\)[/tex], we get [tex]\(-2 \cdot \log_5(5)\)[/tex].
4. Evaluate the Base Logarithm:
- By definition, [tex]\(\log_5(5) = 1\)[/tex] because 5 to the power of 1 is 5.
5. Calculate the Final Result:
- Now substitute back: [tex]\(-2 \cdot \log_5(5) = -2 \cdot 1 = -2\)[/tex].
So, the value of [tex]\(\log_5 \frac{1}{25}\)[/tex] is [tex]\(-2\)[/tex].
We appreciate you taking the time to read Evaluate the expression without using a calculator tex log 5 frac 1 25 tex tex log 5 frac 1 25 tex. We hope the insights shared have been helpful in deepening your understanding of the topic. Don't hesitate to browse our website for more valuable and informative content!
- Why do authors use plot complications in stories A To resolve all a story s conflicts at once B To increase suspense and interest C
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees.
Rewritten by : Batagu
