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Example Questions
Example Question #31 : Solve Logarithmic Equations
Completely expand this logarithm:
Quotient property:
Product property:
Power property:
Example Question #31 : Solve Logarithmic Equations
Fully expand:
In order to expand the expression, use the log rules of multiplication and division. Anytime a variable is multiplied, the log is added. If the variable is being divided, subtract instead.
When there is a power to a variable when it is inside the log, it can be pulled down in front of the log as a coefficient.
The answer is:
Example Question #61 : Properties Of Logarithms
Expand the following:
To solve, simply remember that when you add logs, you multiply their insides.
Thus,
Example Question #62 : Properties Of Logarithms
Express the following in expanded form.
To solve, simply remember that when adding logs, you multiply their insides and when subtract logs, you divide your insides. You must use this in reverse to solve. Thus,
Example Question #37 : Solve Logarithmic Equations
Completely expand this logarithm:
The answer is not present.
We expand logarithms using the same rules that we use to condense them.
Here we will use the quotient property
and the power property
.
Use the quotient property:
Rewrite the radical:
Now use the power property:
Example Question #33 : Solve Logarithmic Equations
Expand the logarithm
In order to expand the logarithmic expression, we use the following properties
As such
Example Question #103 : Exponential And Logarithmic Functions
Given the equation , what is the value of
? Use the inverse property to aid in solving.
The natural logarithm and natural exponent are inverses of each other. Taking the of
will simply result in the argument of the exponent.
That is
Now, , so
Example Question #1 : Graph Logarithms
What is the domain of the function
The function is undefined unless
. Thus
is undefined unless
because the function has been shifted left.
Example Question #1 : Graph Logarithms
What is the range of the function
To find the range of this particular function we need to first identify the domain. Since we know that
is a bound on our function.
From here we want to find the function value as approaches
.
To find this approximate value we will plug in into our original function.
This is our lowest value we will obtain. As we plug in large values we get large function values.
Therefore our range is:
Example Question #3 : Graph Logarithms
Which of the following logarithmic functions match the provided diagram?
Looking at the diagram, we can see that when ,
. Since
represents the exponent and
represents the product, and any base with an exponent of 1 equals the base, we can determine the base to be 0.5.
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