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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.
Study the statement. 100 = 102. In this statement we say that 10 is the base and 2 is the power or index. Logarithms provide an alternative way of writing a statement such as this. We rewrite it as. log10 100 = 2. This is read as ‘log to the base 10 of 100 is 2’. These alternative forms are shown in Figure 1. index or power. 100 = 102 log 100.
a > 0, a 6= 1 and b > 0 we have: loga b = c , ac = b. What does it mean? First of all the assumptions (restrictions) are important. The number a, called the base of the logarithm, has to be greater than 0 and cannot be equal to 1. The number b (which we take the logarithm of) has to be greater than 0.
Precalculus Tutorials. Introduction to Logarithms. -A logarithm is the inverse function for an exponent; therefore, we will review exponential functions first. Review of Exponential Functions. -An exponential function has the general form ( ) = , where 0 < -b is called the base and x is called the exponent. < 1, or > 1.
The exponential equation x = ba is pronounced "x equals b to the power of a". Conversely, the logarithmic equation log b(x) = a, is pronounced "log base b of x equals a". In both equations, we say that: is the base, is the exponent, and. is the argument.
logarithms allow for the simplification of complex problem situations to basic arithmetic operations. In this unit you will examine the definition and inverse relationship with the exponential function, practice the laws of logarithms, solve logarithmic equations, and explore a
2D Introduction to logarithms. In this section we shall look at an operation which reverses the ef ect of exponentiating (raising to a power) and allows us to fi nd an unknown power. If you are asked to solve. x2 3 f x ≥ 0.