Common logarithm
from class: College Algebra Definition A common logarithm is a logarithm with base 10, often written as $\log_{10}(x)$ or simply $\log(x)$. It is commonly used in scientific calculations and when dealing with exponential growth or decay.
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Predict what's on your test 5 Must Know Facts For Your Next Test The common logarithm of 10 is 1, i.e., $\log(10) = 1$. The common logarithm of 1 is 0, i.e., $\log(1) = 0$. Common logarithms are the inverse functions of base-10 exponential functions. The change of base formula allows conversion between natural logarithms and common logarithms: $\log_a(b) = \frac{\log(b)}{\log(a)}$. $\log(xy) = \log(x) + \log(y)$ and $\log(\frac{x}{y}) = \log(x) - \log(y)$ are key properties used to simplify expressions. Review Questions What is the value of $\log_{10}(100)$? How can you express $\ln(x)$ in terms of common logarithms using the change of base formula? Simplify the expression: $\log(2) + \log(5)$. "Common logarithm" also found in:
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