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Example Question #1 : Express Logarithms In Expanded Form
Expand the following logarithmic expression:
We start expanding our logarithm by using the following property:
Now we have two terms, and we can further expand the first term with the following property:
Now we only have two logarithms left with nonlinear terms, which we can expand using one final property:
Using this property on our two terms with exponents, we obtain the final expanded expression:
Example Question #81 : Exponential And Logarithmic Functions
, use the quotient property of logs.
The quotient property states:
Substituting in our given information we get:
Example Question #82 : Exponential And Logarithmic Functions
Which of the following correctly expresses the following logarithm in expanded form?
Begin by recalling a few logarithm rules:
1) When adding logarithms of like base, multiply the inside.
2) When subtracting logarithms of like base, subtract the inside.
3) When multiplying a logarithm by some number, raise the inside to that power.
Keep these rules in mind as we work backward to solve this problem:
Using rule 2), we can get the following:
Next, use rule 1) on the first part to get:
Finally, use rule 3) on the second and third parts to get our final answer:
Example Question #83 : Exponential And Logarithmic Functions
Express in its expanded, simplified form.
Using the properties of logarithms, expand the logrithm one step at a time:
When expanding logarithms, division becomes subtration, multiplication becomes division, and exponents become coefficients.
Example Question #84 : Exponential And Logarithmic Functions
Expand this logarithm:
None of the other answers.
Use the Quotient property of Logarithms to express on a single line:
Use the Product property of Logarithms to expand the two terms further:
Finally use the Power property of Logarithms to remove all exponents:
The expression is now fully expanded.
Example Question #85 : Exponential And Logarithmic Functions
Expand the following logarithm:
Expand the following logarithm:
To expand this log, we need to keep in mind 3 rules:
1) When dividing within a , we need to subtract
2) When multiplying within a , we need to add
3) When raising to a power within a , we need to multiply by that number
These will make more sense once we start applying them.
First, let's use rule number 1
Next, rule 2 sounds good.
Finally, use rule 3 to finish up!
Making our answer
Example Question #86 : Exponential And Logarithmic Functions
Completely expand this logarithm:
Example Question #87 : Exponential And Logarithmic Functions
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 #88 : Exponential And Logarithmic Functions
Expand the following:
To solve, simply remember that when you add logs, you multiply their insides.
Example Question #2 : Express Logarithms In Expanded Form
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,