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Precalculus : Graph Logarithms

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Example Question #11 : Graph Logarithms

Evaluate:

$\log_2256$

Possible Answers:

$\log_2256$

Correct answer:

Explanation:

To evaluate, you must convert 256 to a power of 2. Then the log and 2 will cancel to leave you with your answer.

256=2^8

$\log_22^8=8$

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Example Question #12 : Graph Logarithms

Which of these is a correct method for evaluating $log_{4}8$ ?

Possible Answers:

log8-log4

log_84

log2-log2^3

log8+log4

$\frac{log_24}{log_28}$

Correct answer:

$\frac{log_24}{log_28}$

Explanation:

When evaluating a log you are asking what power your base must be raised by to get your argument.

If you cannot directly figure that out you can use a change of base formula instead.

$log_ab=\frac{log_cb}{log_ca}$

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Example Question #1203 : Pre Calculus

Evaluate this logarithm: $f(x)=\log_{3}x,\hspace{1mm}x=243$

Possible Answers:

$f(243)=\log_{3}243=3$

$f(243)=\log_{3}243=8$

$f(243)=\log_{3}243=3$

$f(243)=\log_{3}243=5$

$f(243)=\log_{3}243=6$

Correct answer:

$f(243)=\log_{3}243=5$

Explanation:

It is important to remember a logarithm is really just an exponent. In fact when you see $\log_{a}x$ remember that the expression is only asking what exponent must "a" be raised to in order to obtain "x"!

$f(243)=\log_{3}243$

Now that we have substituted the value of x reread the problem by the rule above. What power must 3 be raised to in order to obtain 243?

3^2=9

3^3=27

3^4=81

3^5=243

5 is the power to which 3 must be raised to obtain 243.

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Example Question #13 : Graph Logarithms

Evaluate the logarithm

$\small \log_4 (\frac{1}{4}) \,$

Possible Answers:

$\small -\frac{3}4{}$

$\small \frac{1}{16}$

Correct answer:

Explanation:

Given the property

$\small \log_a a^b = b$

and because

$\small 4^{-1} = \frac{1}{4}$

we obtain that

$\small \small \log_4 (\frac{1}{4}) =-1$

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Example Question #14 : Graph Logarithms

Evaluate to four decimal places: $\log _{5} 7$

Possible Answers:

0.1690

0.8271

1.2091

0.1461

4.8928

Correct answer:

1.2091

Explanation:

Using a calculator, evaluate $\frac{\log7}{\log5} \approx 1.2091$

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Example Question #15 : Graph Logarithms

Evaluate to 4 decimal places: $\log _{4 } 80$

Possible Answers:

0.3164

48.1648

0.4758

3.1610

1.3010

Correct answer:

3.1610

Explanation:

To evaluate, use a calculator to find $\frac{\log80}{\log4} \approx 3.1610$

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Example Question #1214 : Pre Calculus

Evaluate the following:

$\log_{2}4-\log_{3}27$

Possible Answers:

Correct answer:

Explanation:

To solve, simply find the matching base and use properties of logs to simplify.

Some properties of logs include the following:

1) $log_bx=y\Rightarrow b^y=x$

2) $logx^y\Rightarrow ylogx$

3) log_xx=1

Thus,

$\\ \log_{2}4-\log_{3}27\\ \\ =\log_{2}2^2-\log_{3}3^3\\ \\=2\log_{2}2-3\log_{3}3\\ \\=2-3\\ \\=-1$

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Example Question #16 : Graph Logarithms

Evaluate the following:

$2\log2+\log\frac{5}{2}$

Possible Answers:

$\frac{5}{2}$

Correct answer:

Explanation:

To solve, remember the following rules for logarithms.

${x}\log{a}=\log{a^x}$

$\log{a}+\log{b}=\log{ab}$

Thus,

$2\log2+\log\frac{5}{2}=\log{2^2}+\log{\frac{5}{2}}=\log{\frac{4*5}{2}}=\log{10}=1$

Remember, if a base isn't specified, it is 10.

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Precalculus : Graph Logarithms

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #11 : Graph Logarithms

Example Question #12 : Graph Logarithms

Example Question #1203 : Pre Calculus

Example Question #13 : Graph Logarithms

Example Question #14 : Graph Logarithms

Example Question #15 : Graph Logarithms

Example Question #1214 : Pre Calculus

Example Question #16 : Graph Logarithms

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