Monday, November 12, 2007

Logarithms and Exponents

Hey everyone, this is JessiccaI as scribe for today's class. At the beginning of class we started off with two questions.

The first question:

Using the Product law, you can multiply the powers of the logs together.

In the second line, you notice that the equation is in exponential form. You put it into exponential form since you have the base and the exponent already. Once both sides have been multiplied out, you make everything equal to zero. Since it doesn't factor well, you can pull out the Quadratic Formula to solve what x is:

You can always check if your answers are correct if you plug them correctly into you calculator or if you approximate the values of x. Note: if you plug it into you calculator make sure the you've made the whole equation into base 10 (the common log).

The second question we got was:

This almost the exact same thing as the one above. The only exception being that both sides of the equations have logs. The answer for this question:

The "antilog" on the third line undoes the log on both sides of the equation, so you're left with a quadratic. The -1 was rejected because when plugged in to the original equation Log(base)2 (of) (x-2), it becomes a negative. No number can equal a negative no matter how many times the number gets multiplied by itself.

After finishing these questions we then looked at the Properties of Exponential Functions and the Properties of Logarithmic Functions. Refer to November 12, 2007 slides to see the graphs and properties of the graphs. Remember if you want to see a log graph on the calculator or calculate values, make everything to base 10 or, in other words, use the Change of Base Law we learned to do on Friday.

The next scribe is

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