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Learn the eight (8) log rules or laws to help you evaluate, expand, condense, and solve logarithmic equations. Try out the log rules practice problems for an even better understanding.
- Expanding Logarithms
Expanding Logarithmic Expressions. When you are asked to...
- Exponent Rules
Rules or Laws of Exponents. In algebra, it’s crucial to...
- Logarithm Explained
Example 1: Solve for y in logarithmic equation log 3 3 = y....
- Expanding Logarithms
ln(x) = log e (x) When e constant is the number: or . See: Natural logarithm. Inverse logarithm calculation. The inverse logarithm (or anti logarithm) is calculated by raising the base b to the logarithm y: x = log-1 (y) = b y. Logarithmic function. The logarithmic function has the basic form of: f (x) = log b (x) Logarithm rules
In this article, we are going to learn the definition of logarithms, two types of logarithms such as common logarithm and natural logarithm, and different properties of logarithms with many solved examples. Table of contents:
There are mainly 4 important log rules which are stated as follows: product rule: log b mn = log b m + log b n. quotient rule: log b m/n = log b m - log b n. power rule: log b m n = n log b m. change of base rule: log a b = (log c b) / (log c a)
The laws of logarithms are algebraic rules that allow for the simplification and rearrangement of logarithmic expressions. The 3 main logarithm laws are: The Product Law: log (mn) = log (m) + log (n). The Quotient Law: log (m/n) = log (m) – log (n). The Power Law: log (m k) = k·log (m).
What are Logs in Math? Logs are the other way of writing exponent. The formula for conversion between exponential and log forms is: b x = a ⇔ log b a = x. Logarithms are very useful in solving equations involving exponents.
Logarithmic scales reduce wide-ranging quantities to smaller scopes. For example, the decibel (dB) is a unit used to express ratio as logarithms, mostly for signal power and amplitude (of which sound pressure is a common example). In chemistry, pH is a logarithmic measure for the acidity of an aqueous solution.