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(a) Convert the following to logarithmic form. \[ 5^{3}=125 \] 3

Ask by Lane Mccoy. in the United States
Nov 06,2024

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\(\log_{5}(125) = 3\)

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To express the equation \(5^3 = 125\) in logarithmic form, we rewrite it as \(\log_5(125) = 3\). This means that the base 5 raised to the power of 3 gives us 125, which is a nifty way to understand the relationship between exponentiation and logarithms! Logarithmic forms are not just for math geeks; they pop up everywhere! For instance, scientists often use logarithmic scales to measure the intensity of earthquakes (Richter scale) or sound intensity (decibels). By transforming exponential relationships into logarithmic ones, complex phenomena can be analyzed and understood more easily. How cool is that?

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