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Algebra II : Simplifying Logarithms

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Example Question #21 : Simplifying 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:

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

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

$log_{10}(7)$

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Example Question #2991 : Algebra Ii

Subtract the logarithms:

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

Possible Answers:

$log_{10}(7)$

$log_{10}(15)$

$log_{10}(5)$

$log_{10}(20)$

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:

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

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

$log_{10}(5)$

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Example Question #11 : Adding And Subtracting Logarithms

Subtract the logarithms:

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

Possible Answers:

$log_{10}(20)$

$log_{10}(44)$

$log_{10}(11)$

$log_{10}(15)$

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:

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

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

$log_{10}(11)$

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Example Question #12 : Adding And Subtracting Logarithms

Subtract the logarithms:

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

Possible Answers:

$log_{10}(7)$

$log_{10}(3)$

$log_{10}(2)$

$log_{10}(7/4)$

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:

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

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

$log_{10}(7/4)$

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Example Question #13 : Adding And Subtracting Logarithms

Subtract the logarithms:

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

Possible Answers:

$log_{10}(8)$

$log_{10}(3/11)$

$log_{10}(1/4)$

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:

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

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

$log_{10}(3/11)$

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Example Question #14 : Adding And Subtracting Logarithms

Subtract the logarithms:

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

Possible Answers:

$log_{10}(2/5)$

$log_{10}(3)$

$log_{10}(2)$

$log_{10}(1/5)$

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:

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

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

$log_{10}(2/5)$

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Example Question #15 : Adding And Subtracting Logarithms

Add the logarithms:

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

Possible Answers:

$log_{10}(8)$

$log_{10}(2)$

$log_{10}(12)$

$log_{10}(15)$

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:

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

$log_{10}(5*3)$

$log_{10}(15)$

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Example Question #21 : Adding And Subtracting Logarithms

Add the logarithms:

$log_{10}(7)+log_{10}(6)$

Possible Answers:

$log_{10}(13)$

$log_{10}(21)$

$log_{10}(42)$

$log_{10}(24)$

Correct answer:

$log_{10}(42)$

Explanation:

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

$log_{10}(7)+log_{10}(6)$

$log_{10}(7*6)$

$log_{10}(42)$

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Example Question #22 : Adding And Subtracting Logarithms

Add the logarithms:

$log_{10}(12)+log_{10}(4)$

Possible Answers:

$log_{10}(42)$

$log_{10}(24)$

$log_{10}(16)$

$log_{10}(48)$

Correct answer:

$log_{10}(48)$

Explanation:

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

$log_{10}(12)+log_{10}(4)$

$log_{10}(12*4)$

$log_{10}(48)$

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Example Question #23 : Adding And Subtracting Logarithms

Simplify the following expression:

$\log_{3}6+\log_{3}4-\log_{4}5$

Possible Answers:

$\log_310+\log_45$

$\log_310-\log_45$

$\log_324-\log_45$

$\log_324+\log_45$

Correct answer:

$\log_324-\log_45$

Explanation:

The furthest we can simplify the given expression is combining the two terms with the same base by multiplying the numbers on the "outside" of the logarithm (addition becomes multiplication when performing logarithmic operations).

Our final answer is therefore

$\log_324-\log_45$

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Algebra II : Simplifying Logarithms

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #21 : Simplifying Logarithms

Example Question #2991 : Algebra Ii

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 #21 : Adding And Subtracting Logarithms

Example Question #22 : Adding And Subtracting Logarithms

Example Question #23 : Adding And Subtracting Logarithms

All Algebra II Resources

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