Question
Write the exponential equation in logarithmic form. For example, the logarithmic form of \( 2^{3}=8 \) is \( \log _{2} 8=3 \). Need Help? Read It SUBMIT ANSWER S9
Ask by Allan Curry. in the United States
Jan 23,2025
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Answer
To convert an exponential equation to its logarithmic form, use the definition: if \( b^{y} = x \), then \( \log_{b} x = y \). For example, \( 2^{3} = 8 \) becomes \( \log_{2} 8 = 3 \).
Solution
It looks like you'd like to convert an exponential equation into its logarithmic form, similar to the example you provided:
**Exponential Form:** \( 2^{3} = 8 \)
**Logarithmic Form:** \( \log_{2} 8 = 3 \)
To assist you effectively, please provide the specific exponential equation you'd like to convert. However, I can show you the general process with another example:
**Example:**
**Exponential Equation:** \( 5^{x} = 125 \)
**Logarithmic Form:** To convert this, you can use the definition of a logarithm, which states that if \( b^{y} = x \), then \( \log_{b} x = y \).
Applying this to the example:
\[
\log_{5} 125 = x
\]
So, \( \log_{5} 125 = x \) is the logarithmic form of \( 5^{x} = 125 \).
**Steps to Convert Exponential to Logarithmic Form:**
1. **Identify the base (b):** This is the number that's raised to a power in the exponential equation.
2. **Identify the result (x):** This is the number that the base is raised to.
3. **Identify the exponent (y):** This is the power to which the base is raised.
4. **Apply the logarithm definition:** Convert \( b^{y} = x \) to \( \log_{b} x = y \).
**Another Example:**
**Exponential Equation:** \( 10^{2} = 100 \)
**Logarithmic Form:** \( \log_{10} 100 = 2 \)
Feel free to provide the specific equation you need help with, and I'd be happy to convert it for you!
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Simplify this solution The Deep Dive
To convert the exponential equation \( 5^{2} = 25 \) into logarithmic form, you would express it as \( \log_{5} 25 = 2 \). This means that 5 raised to the power of 2 equals 25, which is highlighted in the logarithmic format. Understanding logarithmic forms can be super handy in various scenarios! For example, they are often used in real-life applications such as calculating the pH levels in chemistry, determining the decibel level of sounds, or even analyzing the growth of populations in biology. You’ll see that logarithms are all around us, serving crucial roles in a multitude of fields!
