Logarithms of negative numbers are undefined.The logarithm of the base number is equal to 1.No matter what base, the logarithm of 1 is 0.The natural logarithm ln is a logarithm base e.If the logarithm base is not written, the base is 10.The following rules apply when writing numbers in logarithmic form: Here are some examples of working with the natural logarithm. For example, the exponential equation 2 3=8 is written as log 2(8)=3 in logarithmic form. Radioactive decay and half-life is calculated using logarithmsĪny exponential equation of the form a b=c can be written in logarithmic form using log a(c)=b.Computer algorithm efficiency is measured on a logarithmic scale.The strength of a Wi-Fi signal is measured on a logarithmic scale.The focal ratio in photography is a logarithmic scale.The brightness of stars is measured on a logarithmic scale. The Richter scale used to measure earthquakes is on a logarithmic scale.The pH measure of acidity is a logarithmic scale.Decibels are measured on a logarithmic scale. Here are some examples of where logarithms are used in real life: Logarithms can be used to comprehend the size of large numbers, rearrange equations and solve growth and decay problems. The purpose of the logarithmic form is to calculate exponents and solve exponential equations. The 2 is the exponent in the exponential form but it is the answer when written in logarithmic form. The answer to an equation written in logarithmic form is the exponent. This can be written in logarithmic form as. The number inside the log before the equals sign is the value of the base raised to the power of the exponent.įor example, in the exponential equation 3 2 = 9, the 2 is the exponent.The number after the equals sign is the exponent. The base of the log is the number written in subscript next to the word ‘log’.The word log is written to show that the logarithm function is being used.Īn exponential equation contains an exponent (the small number written to the top right of another number).Įquations written in logarithmic form contain three numbers: The same numbers are used but they are written in a different order. The logarithmic form is simply a rearrangement of an equation written in exponential form. The logarithmic form is used to calculate an exponent of an equation. Any exponential equation can be written as a logarithm. It is a rearrangement of the exponential form, a b=c. The logarithmic form is written as log a(c)=b.
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