Precalculus : Express Logarithms in Condensed Form

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #57 : Properties Of Logarithms

Express the log in its expanded form:

Possible Answers:

None of the other answers

Correct answer:

Explanation:

You need to know the Laws of Logarithms in order to solve this problem. The ones specifically used in this problem are the following:

Let's take this one variable at a time starting with expanding z:

Now y:

And finally expand x:

Example Question #58 : Properties Of Logarithms

What is  equivalent to?

Possible Answers:

Correct answer:

Explanation:

Using the properties of logarithms,

the expression can be rewritten as

 

 which simplifies to .

Example Question #59 : Properties Of Logarithms

Find the value of the sum of logarithms by condensing the expression. 

Possible Answers:

Undefined

Correct answer:

Explanation:

By the property of the sum of logarithms,

.

Example Question #1 : Express Logarithms In Condensed Form

Condense the following logarithmic equation:

Possible Answers:

Correct answer:

Explanation:

We start condensing our expression using the following property, which allows us to express the coefficients of two of our terms as exponents:

Our next step is to use the following property to combine our first three terms:

Finally, we can use the following property regarding subtraction of logarithms to obtain the condensed expression:

Example Question #2 : Express Logarithms In Condensed Form

What is another way of writing

 ?

Possible Answers:

Correct answer:

Explanation:

The correct answer is 

Properties of logarithms allow us to rewrite  and  as  and , respectively. So we have

Again, we use the logarithm property

  

to get

Example Question #62 : Properties Of Logarithms

Write the expression in the most condensed form:

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

Use the Power property of Logarithms:

Rewrite the fractional exponent:

Condense into a fraction using the Quotient property of Logarithms:

Example Question #63 : Properties Of Logarithms

Simplify:  

Possible Answers:

Correct answer:

Explanation:

When logs of the same bases are subtracted, the contents of both logs will be divided with each other.  When logs of the same bases are added, then the contents inside the log will be multiplied together.

Example Question #3 : Express Logarithms In Condensed Form

Completely condense the logarithm: .

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

Apply the Power property:

Apply the quotient property:

Example Question #65 : Properties Of Logarithms

Simplify

Possible Answers:

Correct answer:

Explanation:

By the property of the addition of logarithms with the same base

As such

Example Question #4 : Express Logarithms In Condensed Form

Condense the following equation:

Possible Answers:

Cannot simplify

Correct answer:

Explanation:

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

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