Pregunta
24. Express \( g^{x}=8 \) in logarithmic form
Ask by Pearson Gibson. in the United States
Feb 03,2025
Solución de tutoría real
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\( g^{x} = 8 \) in logarithmic form is \( \log_g(8) = x \).
Solución
To express the equation \( g^{x} = 8 \) in logarithmic form, we can follow these steps:
1. Identify the base, exponent, and result in the equation. Here, the base is \( g \), the exponent is \( x \), and the result is \( 8 \).
2. The logarithmic form of an exponential equation \( a^b = c \) is given by \( \log_a(c) = b \).
3. Applying this to our equation \( g^{x} = 8 \), we can rewrite it in logarithmic form as:
\[
\log_g(8) = x
\]
Thus, the expression \( g^{x} = 8 \) in logarithmic form is \( \log_g(8) = x \).
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Simplifique esta solución Beyond the Answer
To express \( g^{x} = 8 \) in logarithmic form, you can rewrite this equation as \( \log_g(8) = x \). This means that \( x \) is the exponent to which the base \( g \) must be raised to yield 8. So, whenever you're dealing with exponentials, remember that converting to logarithmic form is a powerful tool! Now, just think about the implications of this! If you know the values of \( g \) and \( x \), you can easily calculate the output. Conversely, if you only have the output (like 8), you can find the necessary exponent (or \( x \)) by using the logarithm. Pretty neat, right?
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