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# 7-3: Logarithmic Functions as Inverses

Algebra 2 Honors

by

Tweet## Jessica Edrington

on 1 May 2013#### Transcript of 7-3: Logarithmic Functions as Inverses

7-3: Logarithmic Functions as Inverses The logarithm base b of a positive number x is the exponent to which base b must be raised to get x. What is a logarithm? Ex:

Translate into math symbols:

logarithm base 2 of 16 equals 4 A logarithm is the INVERSE of an exponential -- one undoes the other.

The base of the logarithm will be the base of the exponential. Write the given exponential equations as equivalent logarithms. Writing Exponential Equations in Logarithmic Form To evaluate a logarithm:

1. Rewrite it as an equivalent exponential.

2. Write both sides of the equation so that they are exponentials with the same base.

3. If the bases are the same, then the exponents will be equal. Evaluating Logarithms For example... In 1995, an earthquake in Mexico registered 8.0 on the Richter scale.

In 2001, an earthquake of magnitude 6.8 shook Washington state.

How many times more intense was the 1995 earthquake than the 2001 earthquake? Using a Logarithm Scale Use the formula

to compare the intensity levels of earthquakes,

where I is the intensity level and M is the magnitude on the Richter scale. Logarithms can have different bases.

If a base isn't written, then you assume the base is 10. (Base 10 logarithms are called "common logs"). Given a logarithm function, graph the function and describe the domain, range, y-intercept, and asymptotes. Graphing a Logarithmic Function

Full transcriptTranslate into math symbols:

logarithm base 2 of 16 equals 4 A logarithm is the INVERSE of an exponential -- one undoes the other.

The base of the logarithm will be the base of the exponential. Write the given exponential equations as equivalent logarithms. Writing Exponential Equations in Logarithmic Form To evaluate a logarithm:

1. Rewrite it as an equivalent exponential.

2. Write both sides of the equation so that they are exponentials with the same base.

3. If the bases are the same, then the exponents will be equal. Evaluating Logarithms For example... In 1995, an earthquake in Mexico registered 8.0 on the Richter scale.

In 2001, an earthquake of magnitude 6.8 shook Washington state.

How many times more intense was the 1995 earthquake than the 2001 earthquake? Using a Logarithm Scale Use the formula

to compare the intensity levels of earthquakes,

where I is the intensity level and M is the magnitude on the Richter scale. Logarithms can have different bases.

If a base isn't written, then you assume the base is 10. (Base 10 logarithms are called "common logs"). Given a logarithm function, graph the function and describe the domain, range, y-intercept, and asymptotes. Graphing a Logarithmic Function