Every positive number, y, can be expressed as 10 raised to some power, x. This is the black dot in the graph. Here is the formal definition of the base 10 logarithm function.

First use the power property, then use the product property of logarithms.

If you need to use a calculator to evaluate an expression with a different base, you can apply the change-of-base formulas first. Using this change of base, we typically write a given exponential or logarithmic function in terms of the natural exponential and natural logarithmic functions.

Proof For the first change-of-base formula, we begin by making use of the power property of logarithmic functions.

Hint Use the change of base to rewrite this expression in terms of expressions involving the natural logarithm function. The scale is a base logarithmic scale, and it can be described as follows: A way of measuring the intensity of an earthquake is by using a seismograph to measure the amplitude of the earthquake waves.

Consider an earthquake that measures 8 on the Richter scale and an earthquake that measures 7 on the Richter scale. That is, the first earthquake is times more intense than the second earthquake. How can we use logarithmic functions to compare the relative severity of the magnitude 9 earthquake in Japan in with the magnitude 7.

Solution To compare the Japan and Haiti earthquakes, we can use an equation presented earlier:Review of Trigonometric, Logarithmic, and Exponential Functions In this tutorial, we review trigonometric, logarithmic, and exponential functions with a focus on those properties which will be useful in future math and science applications.

11 Exponential and Logarithmic Functions Concepts: • Exponential Functions the a value, in an exponential function is positive and not equal to 1. Note that b(x) and c(x) in Example are not exponential functions. • Write a function to express the total number, P, of bacteria are in .

Algebra II Notes Exponential and Log Functions Unit – Alg II Notes Unit ‐ Exponential and Log Functions Page 7 of 31 01/10/ Sample SAT Question(s): Taken from College Board online practice problems. Remember that since the logarithmic function is the inverse of the exponential function, the domain of logarithmic function is the range of exponential function, and vice versa.

In general, the function y = log b x where b, x > 0 and b ≠ 1 is a continuous and one-to-one function.

Learn about logarithms, which are the inverses of exponents. Use logarithms to solve various equations. Then analyze both logarithmic and exponential functions and their graphs. Writing an Exponential Function Write an exponential function y = abx whose graph passes through (1, 6) and (3, 24).

Chapter 8 Exponential and Logarithmic Functions Finding an Exponential Model The table gives the number y (in millions) of cell-phone subscribers from to.

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Logarithmic Functions