Section 1.4 Logarithmic Functions. Find x for the following: How about now?

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Presentation transcript:

Section 1.4 Logarithmic Functions

Find x for the following: How about now?

In the previous example we needed to solve for the input Since exponential functions are 1-1, they have an inverse The inverse of an exponential function is called the logarithm function or the log function In other words

Now our exponential equation may not always have a base of 10. The general definition of log is Often we will deal with the natural base which gives way to the natural log

Properties of the common Logarithm

The Natural Logarithm

Evaluate

Example The median house price in the Phoenix area in 2000 was about $120,000. In 2005, the median house price rose to about $250,000. Assuming the growth was exponential, create a model for the median house price as a function of time. –Hint: Use t = 0 to correspond to the year –According to the model, when will the median house price be $350,000?