Logarithmic functions as Inverses
You may wonder about the title of this lesson and what it means. The logarithmic function (log function) has an inverse relationship with the exponential function we studied in lesson 8.1
Think about the graph for y = 2^x.
Now, look on page 440 of your text and look at the graph under objective 2.
Notice the exponential funtion is sketched in red ink and the logarithmic function is sketched in blue ink.
Now look at the graph in example 5. What other equation has been graphed in green?
In Alg. 2, you learned that a function and its inverse are "SYMMETRIC" about the line y = x. This means that if you fold the graph on the line y = x, the exponential function and the log function fold on top of each other.
ISN'T MATH NEAT... Again, looking at the graph in example 5, look
at the asymptote for y = log (base 2) of x.
The asymptote for the logarithmic function is the y axis or the line x = 0.
As you remember, the asymptote for the exponential function is the line y = 0.
Tonight's assignment: Post a comment and answer the following QUESTIONS?????????????????????????????????????????
1. In this lesson, what did you learn about a common log?
2. How do you change an exponential equation (y=b^x) to a log equation?
3. How do you change a log equation to an exponential equation?
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20 comments:
It is a logarithm that uses base 10
it is a loarithm that uses a base of 10
you take y=b^x and change it to logb y=x
1.The common log is a logarithm that uses the base of 10.
2.You change y=b^x to logb y=x
3.The logarithmic function is the inverse of an exponential function. y=logbx as the inverse of y=b^x
ANSWERS:
1)The common log uses a base of 10.
2)Subscript b Y = X
3)Convert to exponential form, write each side using a certain base, power property of exponents, set the exponents equal to each other, solve for X.
I murked this lesson :D
3. you take the inverse of the log equation which gives you y=b^x. Sorry I left 3 different comments. =)
1. A common logarithm is a logarithm that uses base 10.
2. You change y=b^x to logb y=x
3. Y=logbx the inverse is y=b^x
1.The common log is a logarithm that uses the base of 10.
2.You change y=b^x to logb y=x
3. log to exponetial -- y=logbx as the inverse of y=b^x -- you do the opposite.
1.The common log is a logarithm that uses the base of 10.
2.You change y=b^x to logb y=x and plug in the numbers.
3.The logarithmic function is the inverse of an exponential function. y=logbx as the inverse of y=b^x.
2. you change y= (b)^x ; logb y=x
3. change y=logbx to y=b^x
1) A common logarithm is a logarithm that uses base 10.
2) You change y=b^x to logb y=x.
3) Use the inverse of the log equation. (y=b^x.)
Caitlin Goode:
1) Common logarithm is a logarithm that uses base 10.
2) Change y=b^x to logb y=x
3) Log is the inverse of an exponential. y=logbx its inverse y=b^x
1. A logarithm that uses the base of 10.
2. change y=b^x to logb y=x
3. this function is an inverse of an expontential function. Basically, you put it in exponential form, set exponents eual, solve for x... rewrite function.
It is a logarithm and it uses the base 10
It is changed y=b^x to logb y=x
the function is an inverse of the exponential function. logbx=y is the inverse of y=b^x
2. Subscript b under log and multiply by y. Set equal to x.
y=b^x --> logb(y)=x
Matt G.
1. common log uses 10 as its base
2.take y=bx to logby=x
3. its the inverse of the exponential function.
-Drew K.
got on here to see if anyone needed help mrs. snipes... guess not =)
Thanks Erica :)
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