Algebra II : Adding and Subtracting Logarithms

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #31 : Adding And Subtracting Logarithms

Simplify the log:  

Possible Answers:

Correct answer:

Explanation:

This question will require the product and quotient properties.

Product:  

Quotient:  

Evaluate the first two terms according to the formula.

Add using the product property: 

The answer is:  

Example Question #32 : Adding And Subtracting Logarithms

Combine all logs into a single log:  

Possible Answers:

Correct answer:

Explanation:

Evaluate the first term.  It can be rewritten by moving the coefficient as a power of the integer inside the log.

According to the product property of logs, when logs are added, the values inside the log can be multiplied together so that the log can be combined as one unit.

Subtract this log with .

According to the division property of logs, when two log values are subtracted, we can combine the logs and divide the numbers.

The answer is:  

Example Question #33 : Adding And Subtracting Logarithms

Add the following logs:  

Possible Answers:

Correct answer:

Explanation:

The log has a default base of 10.  Recall that if:

Evaluate each term.

 since .

 since .

Add the terms to simplify.

The answer is:  

Example Question #34 : Adding And Subtracting Logarithms

Combine as one log:  

Possible Answers:

Correct answer:

Explanation:

According to log properties, when there is a coefficient in front of a log, the coefficient can be transferred as the exponent of the inner value of log.

Convert the expression.

Simplify the terms.

When the logs of a same base are added, we can multiply the inner terms together to combine the log as one whole.

The answer is:  

Example Question #35 : Adding And Subtracting Logarithms

Add the logs:  

Possible Answers:

Correct answer:

Explanation:

Combine the logs together using the log properties.

This is also equivalent to:

OR:  

The answer is:  

Example Question #36 : Adding And Subtracting Logarithms

Combine as one log:  

Possible Answers:

Correct answer:

Explanation:

Whenever logs of the same bases are added, the terms inside the logs can be multiplied.

Likewise, when logs are subtracted, they are divided instead.

Evaluate the first two logs.

The expression becomes .

Divide the numbers inside.

The answer is:  

Example Question #37 : Adding And Subtracting Logarithms

Combine as one log, if possible:  

Possible Answers:

Correct answer:

Explanation:

According to the log property, we can combine the expression as one log

Be careful not to simplify  and subtract the quantity of the log and the integer.

The answer is:  

Example Question #38 : Adding And Subtracting Logarithms

Combine as one log:  

Possible Answers:

Correct answer:

Explanation:

According to log rules, the coefficients of the logs can be raised as powers for the inner quantity of the log.  Rewrite the terms.

Subtract the .

The answer is:  

Example Question #39 : Adding And Subtracting Logarithms

Combine as one log:  

Possible Answers:

Correct answer:

Explanation:

According to the log property, we can bring coefficients of logs as powers of the inner term of the log.

Rewrite the expression.

The answer is: 

Example Question #40 : Adding And Subtracting Logarithms

Add the following logs:  

Possible Answers:

Correct answer:

Explanation:

According to log properties, when there is a coefficient in front of the log, the coefficient can be used as the exponent for the inner quantity of the log.

Rewrite the expressions.

The expression becomes: 

When logs are added, they can be combined into one log by multiplying the two quantities.

When logs are subtracted, the quantities are then divided.

Reduce the fraction.

The answer is:  

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