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Algebra II : Logarithms

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Example Questions

Example Question #91 : Logarithms

Subtract the logarithms:

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

Possible Answers:

$log_{10}(20)$

$log_{10}(5)$

$log_{10}(15)$

$log_{10}(7)$

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 #92 : Logarithms

Subtract the logarithms:

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

Possible Answers:

$log_{10}(20)$

$log_{10}(44)$

$log_{10}(15)$

$log_{10}(11)$

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 #93 : Logarithms

Subtract the logarithms:

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

Possible Answers:

$log_{10}(2)$

$log_{10}(7/4)$

$log_{10}(7)$

$log_{10}(3)$

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 #94 : 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:

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

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

$log_{10}(3/11)$

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Example Question #95 : 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:

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

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

$log_{10}(2/5)$

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Example Question #96 : Logarithms

Add the logarithms:

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

Possible Answers:

$log_{10}(12)$

$log_{10}(2)$

$log_{10}(15)$

$log_{10}(8)$

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:

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

$log_{10}(5*3)$

$log_{10}(15)$

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Example Question #97 : Logarithms

Add the logarithms:

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

Possible Answers:

$log_{10}(13)$

$log_{10}(21)$

$log_{10}(24)$

$log_{10}(42)$

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 #98 : Logarithms

Add the logarithms:

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

Possible Answers:

$log_{10}(48)$

$log_{10}(24)$

$log_{10}(16)$

$log_{10}(42)$

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 #99 : 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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Example Question #31 : Simplifying Logarithms

If f(x)=log(x+4) and g(x)=log(x-3) , what is f(x)+g(x) ?

Possible Answers:

log(x^2 - 12)

$e^{2x+1}$

log(x^2 +x -12)

log(x^2 +7x +12)

log(2x+1)

Correct answer:

log(x^2 +x -12)

Explanation:

When adding logarithms, you multiply the terms inside the log functions. For this problem you would have:

(x+4)(x-3)

At this point, you FOIL (First, Outer, Inner, Last) the terms to get:

x^2 -3x +4x -12

You then collect the like terms together:

x^2 +x -12

Remember, these terms were originally in a log function, so to get our answer we need to put them back in one:

log(x^2 + x - 12)

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Algebra II : Logarithms

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #91 : Logarithms

Example Question #92 : Logarithms

Example Question #93 : Logarithms

Example Question #94 : Logarithms

Example Question #95 : Logarithms

Example Question #96 : Logarithms

Example Question #97 : Logarithms

Example Question #98 : Logarithms

Example Question #99 : Logarithms

Example Question #31 : Simplifying Logarithms

All Algebra II Resources

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