We're glad you stopped by Write in logarithmic form tex frac 1 25 5 2 tex The logarithmic form is tex log 5 left frac 1 25 right 2 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 :
Sure, let's convert the equation [tex]\(\frac{1}{25} = 5^{-2}\)[/tex] into logarithmic form step by step!
1. Understand the Exponential Form: The given equation [tex]\(\frac{1}{25} = 5^{-2}\)[/tex] is in exponential form. This tells us that [tex]\(5\)[/tex] raised to the power of [tex]\(-2\)[/tex] equals [tex]\(\frac{1}{25}\)[/tex].
2. Identify the Base, Exponent, and Result:
- The base is the number being raised to a power, which is [tex]\(5\)[/tex].
- The exponent (power) is [tex]\(-2\)[/tex].
- The result is [tex]\(\frac{1}{25}\)[/tex].
3. Convert to Logarithmic Form: In general, if the exponential form is [tex]\(b^e = r\)[/tex], then the logarithmic form is [tex]\(\log_b(r) = e\)[/tex].
- Here, [tex]\(b\)[/tex] is [tex]\(5\)[/tex], [tex]\(e\)[/tex] is [tex]\(-2\)[/tex], and [tex]\(r\)[/tex] is [tex]\(\frac{1}{25}\)[/tex].
4. Write the Logarithmic Equation: Substitute the values into the logarithmic form:
[tex]\[
\log_5\left(\frac{1}{25}\right) = -2
\][/tex]
So, the logarithmic form of the equation [tex]\(\frac{1}{25} = 5^{-2}\)[/tex] is [tex]\(\log_5\left(\frac{1}{25}\right) = -2\)[/tex].
1. Understand the Exponential Form: The given equation [tex]\(\frac{1}{25} = 5^{-2}\)[/tex] is in exponential form. This tells us that [tex]\(5\)[/tex] raised to the power of [tex]\(-2\)[/tex] equals [tex]\(\frac{1}{25}\)[/tex].
2. Identify the Base, Exponent, and Result:
- The base is the number being raised to a power, which is [tex]\(5\)[/tex].
- The exponent (power) is [tex]\(-2\)[/tex].
- The result is [tex]\(\frac{1}{25}\)[/tex].
3. Convert to Logarithmic Form: In general, if the exponential form is [tex]\(b^e = r\)[/tex], then the logarithmic form is [tex]\(\log_b(r) = e\)[/tex].
- Here, [tex]\(b\)[/tex] is [tex]\(5\)[/tex], [tex]\(e\)[/tex] is [tex]\(-2\)[/tex], and [tex]\(r\)[/tex] is [tex]\(\frac{1}{25}\)[/tex].
4. Write the Logarithmic Equation: Substitute the values into the logarithmic form:
[tex]\[
\log_5\left(\frac{1}{25}\right) = -2
\][/tex]
So, the logarithmic form of the equation [tex]\(\frac{1}{25} = 5^{-2}\)[/tex] is [tex]\(\log_5\left(\frac{1}{25}\right) = -2\)[/tex].
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