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Algebra II : Adding and Subtracting Logarithms

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #321 : Mathematical Relationships And Basic Graphs

Add the logarithms:

$log_{10}(2)+log_{10}(7)$

Possible Answers:

$log_{10}(12)$

$log_{10}(14)$

$log_{10}(4)$

$log_{10}(9)$

Correct answer:

$log_{10}(14)$

Explanation:

When adding logarithms of the same base, all you have to do is multiply the numbers inside the function as shown below:

$log_{10}(2)+log_{10}(7)$

$log_{10}(2*7)$

$log_{10}(14)$

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Example Question #322 : Mathematical Relationships And Basic Graphs

Add the logarithms:

$log_{10}(12)+log_{10}(3)$

Possible Answers:

$log_{10}(16)$

$log_{10}(9)$

$log_{10}(15)$

$log_{10}(36)$

Correct answer:

$log_{10}(36)$

Explanation:

When adding logarithms of the same base, all you have to do is multiply the numbers inside the function as shown below:

$log_{10}(12)+log_{10}(3)$

$log_{10}(12*3)$

$log_{10}(36)$

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Example Question #11 : Adding And Subtracting Logarithms

Add the logarithms:

$log_{10}(5)+log_{10}(4)$

Possible Answers:

$log_{10}(20)$

$log_{10}(2)$

$log_{10}(9)$

$log_{10}(12)$

Correct answer:

$log_{10}(20)$

Explanation:

When adding logarithms of the same base, all you have to do is multiply the numbers inside the function as shown below:

$log_{10}(5)+log_{10}(4)$

$log_{10}(5*4)$

$log_{10}(20)$

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Example Question #12 : Adding And Subtracting Logarithms

Subtract the logarithms:

$log_{10}(14)-log_{10}(2)$

Possible Answers:

$log_{10}(28)$

$log_{10}(7)$

$log_{10}(3)$

$log_{10}(12)$

Correct answer:

$log_{10}(7)$

Explanation:

When subtracting logarithms of the same base, all you have to do is divide the numbers inside the function as shown below:

$log_{10}(14)-log_{10}(2)$

$log_{10}(14\div 2)$

$log_{10}(7)$

Report an Error

Example Question #13 : Adding And Subtracting Logarithms

Subtract the logarithms:

$log_{10}(25)-log_{10}(5)$

Possible Answers:

$log_{10}(20)$

$log_{10}(15)$

$log_{10}(7)$

$log_{10}(5)$

Correct answer:

$log_{10}(5)$

Explanation:

When subtracting logarithms of the same base, all you have to do is divide the numbers inside the function as shown below:

$log_{10}(25)-log_{10}(5)$

$log_{10}(25\div 5)$

$log_{10}(5)$

Report an Error

Example Question #14 : Adding And Subtracting Logarithms

Subtract the logarithms:

$log_{10}(22)-log_{10}(2)$

Possible Answers:

$log_{10}(15)$

$log_{10}(44)$

$log_{10}(11)$

$log_{10}(20)$

Correct answer:

$log_{10}(11)$

Explanation:

When subtracting logarithms of the same base, all you have to do is divide the numbers inside the function as shown below:

$log_{10}(22)-log_{10}(2)$

$log_{10}(22\div 2)$

$log_{10}(11)$

Report an Error

Example Question #15 : Adding And Subtracting Logarithms

Subtract the logarithms:

$log_{10}(7)-log_{10}(4)$

Possible Answers:

$log_{10}(3)$

$log_{10}(7)$

$log_{10}(2)$

$log_{10}(7/4)$

Correct answer:

$log_{10}(7/4)$

Explanation:

When subtracting logarithms of the same base, all you have to do is divide the numbers inside the function as shown below:

$log_{10}(7)-log_{10}(4)$

$log_{10}(7\div 4)$

$log_{10}(7/4)$

Report an Error

Example Question #16 : Adding And Subtracting Logarithms

Subtract the logarithms:

$log_{10}(3)-log_{10}(11)$

Possible Answers:

$log_{10}(1/4)$

$log_{10}(8)$

$log_{10}(3/11)$

Correct answer:

$log_{10}(3/11)$

Explanation:

When subtracting logarithms of the same base, all you have to do is divide the numbers inside the function as shown below:

$log_{10}(3)-log_{10}(11)$

$log_{10}(3\div 11)$

$log_{10}(3/11)$

Report an Error

Example Question #17 : Adding And Subtracting Logarithms

Subtract the logarithms:

$log_{10}(2)-log_{10}(5)$

Possible Answers:

$log_{10}(2/5)$

$log_{10}(2)$

$log_{10}(3)$

$log_{10}(1/5)$

Correct answer:

$log_{10}(2/5)$

Explanation:

When subtracting logarithms of the same base, all you have to do is divide the numbers inside the function as shown below:

$log_{10}(2)-log_{10}(5)$

$log_{10}(2\div 5)$

$log_{10}(2/5)$

Report an Error

Example Question #18 : Adding And Subtracting Logarithms

Add the logarithms:

$log_{10}(5)+log_{10}(3)$

Possible Answers:

$log_{10}(12)$

$log_{10}(15)$

$log_{10}(2)$

$log_{10}(8)$

Correct answer:

$log_{10}(15)$

Explanation:

When adding logarithms of the same base, all you have to do is multiply the numbers inside the function as shown below:

$log_{10}(5)+log_{10}(3)$

$log_{10}(5*3)$

$log_{10}(15)$

Report an Error

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Algebra II : Adding and Subtracting Logarithms

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #321 : Mathematical Relationships And Basic Graphs

Example Question #322 : Mathematical Relationships And Basic Graphs

Example Question #11 : Adding And Subtracting Logarithms

Example Question #12 : Adding And Subtracting Logarithms

Example Question #13 : Adding And Subtracting Logarithms

Example Question #14 : Adding And Subtracting Logarithms

Example Question #15 : Adding And Subtracting Logarithms

Example Question #16 : Adding And Subtracting Logarithms

Example Question #17 : Adding And Subtracting Logarithms

Example Question #18 : Adding And Subtracting Logarithms

All Algebra II Resources

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