Precalculus : Pre-Calculus
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Example Questions
Example Question #1181 : Pre Calculus
Condense the following equation:
Cannot simplify
Let's use the properties of logarithms to condense this equation. We will use the follwing three properties
Power Rule
Product Rule
Quotient Rule
Let's first use the power rule to rewrite the second term
Then, we'll use the product rule to combine the first threeterms
Lastly, we'll use the quotient rule to combine into one term
Example Question #1181 : Pre Calculus
Express the following in condensed form:
To solve, simply remember that when you add logs, you can multiply their insides and when you subtract them, you can divide.
Thus,
Example Question #1182 : Pre Calculus
Express the following in condensed form:
To solve, simply remember that when add logs, you multiply their insides. Thus,
Example Question #1183 : Pre Calculus
Condense the logarithm
In order to condense the logarithmic expression, we use the following properties
Example Question #1181 : Pre Calculus
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 #1184 : Pre Calculus
Expand
To expand
The quotient property states:
Substituting in our given information we get:
Example Question #1184 : Pre Calculus
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 #1185 : Pre Calculus
Express 
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 #1184 : Pre Calculus
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 #32 : Solve Logarithmic Equations
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 
2) When multiplying within a 
3) When raising to a power within a 
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
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