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logarithmic equation in the original equation. Exclude from the solution set any proposed solution that produces the log of a negative number or the log of 0.
After reading this text and / or viewing the video tutorial on this topic you should be able to: explain what is meant by a logarithm. state and use the laws of logarithms. solve simple equations requiring the use of logarithms.
-Because an exponent will never have negative output (see above), a logarithm can never have negative input. -Because when you raise a number to the 0 power, you get 1, whenever, I repeat, whenever, you put 1 inside a logarithm, you get 0. In other words, 𝐥𝐨𝐠𝒃( )= .
This topic introduces logarithms and exponential equations. Logarithms are used to solve exponential equations, and so are used along with exponential functions when modelling
Properties of Logarithms. -You have probably figured out by now that logarithms are actually exponents! -Due to this, they possess some unique properties that make them even more useful. -In this tutorial we will cover the properties of logarithms and use them to perform expansions and contractions.
So if ab = c. then we say that b is the logarithm of c to the base a, written. = log c . In all of these equations, a and c must be positive numbers; b may be positive, negative or zero. In principle, logarithms can be evaluated by rewriting them as powers. Example. Evaluate log. 2 32. 2x Solution.
1. Review of the Algebra of Exponents. Before discussing logarithms, it is important to remind ourselves about the algebra of exponents, also known as powers. Exponents are a compact notation to express multiplication of a number or variable by itself: = x = 2 ⋅. x x. 3 = x ⋅ x ⋅ x. 9 = x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x ⋅ x.
