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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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10 Diagnostic Tests 630 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #41 : Logarithms

Evaluate .

$5 ^{x} = 12$

Possible Answers:

$x= \frac{ \log 5}{12}$

$x= \log 7$

$x= \frac{ \log 12 }{5}$

$x=\frac{\log 12}{\log 5}$

$x=\frac{ \log 5}{\log 12}$

Correct answer:

$x=\frac{\log 12}{\log 5}$

Explanation:

Take the common logarithm of both sides, and take advantage of the property of the logarithm of a power:

$5 ^{x} = 12$

$\log 5 ^{x} = \log 12$

$x \log 5 = \log 12$

$\frac{x \log 5 }{\log 5 }=\frac{ \log 12}{\log 5}$

$x=\frac{ \log 12}{\log 5}$

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Example Question #2 : Exponential Functions

Which equation is equivalent to:

$\log _{4}\left( \frac{1}{2}\right)=x$

Possible Answers:

$\left(\frac{1}{2}\right)^{4}=x$

$(4)^{x}=\left(\frac{1}{2}\right)^{x}$

$4^{\frac{1}{2}}=x$

$\frac{1^{4}}{2}=x^{4}$

$4^{x}=\frac{1}{2}$

Correct answer:

$4^{x}=\frac{1}{2}$

Explanation:

$log{_{a}}^{b}=x$ , b>0

$\Rightarrow a^{x}=b$

So, ${{log_{4}}^{\frac{1}{2}}}=x\Rightarrow 4^{x}=\frac{1}{2}$

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Example Question #3 : Exponential Functions

$Log_{b}x=y$

What is the inverse of the log function?

Possible Answers:

$b^{y}=x$

$b^{x}=y$

$x^{b}=y$

$b=x\cdot y$

$y^{b}=x$

Correct answer:

$b^{y}=x$

Explanation:

This is a general formula that you should memorize. The inverse of $Log_{b}x=y$ is $b^{y}=x$ . You can use this formula to change an equation from a log function to an exponential function.

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Example Question #42 : Understanding Logarithms

Solve for :

7^b=54

Round to the nearest hundredth.

Possible Answers:

3.21

2.05

Cannot be computed

1.45

0.49

Correct answer:

2.05

Explanation:

To solve this, you need to set up a logarithm. Our exponent is . The logarithm's base is . The value is the operand of the logarithm. Therefore, we can write an equation:

$\log_7{54} = b$

Now, you cannot do this on your calculator. Therefore, using the rule for converting logarithms, you need to change:

$\log_7{54}$

to...

$\frac{\log{54}}{\log{7}}$

You can put this into your calculator and get:

2.04993228926876 , or rounded, 2.05

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Example Question #3 : Logarithms And Exponents

Solve for :

31^r=842

Round to the nearest hundredth.

Possible Answers:

1.73

1.15

0.51

2.31

1.96

Correct answer:

1.96

Explanation:

To solve this, you need to set up a logarithm. Our exponent is . The number of which it is the exponent of (31) is the base. This is the logarithm's base. The value 842 is the operand of the logarithm. Therefore, we can write an equation:

$\log_3_1{842} = r$

Now, you cannot do this on your calculator. Therefore, using the rule for converting logarithms, you need to change:

$\log_3_1{842}$

to...

$\frac{\log{842}}{\log{31}}$

You can put this into your calculator and get:

1.96150410969636 , or rounded, 1.96

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Example Question #4 : Logarithms And Exponents

Solve for :

4^x=6317

Round to the nearest hundredth.

Possible Answers:

3.24

5.65

0.16

2.81

6.31

Correct answer:

6.31

Explanation:

To solve this, you need to set up a logarithm. Our exponent is . The number of which it is the exponent of (4) is the base. This is the logarithm's base. The value 842 is the operand of the logarithm. Therefore, we can write an equation:

$\log_4 {6317} = x$

Now, you cannot do this on your calculator. Therefore, using the rule for converting logarithms, you need to change:

$\log_4 {6317}$

to...

$\frac{\log{6317}}{\log{4}}$

You can put this into your calculator and get:

6.3125119284402 , or rounded, 6.31

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Example Question #1 : Logarithms And Exponents

Solve for :

5^t=40150

Round to the nearest hundredth.

Possible Answers:

6.41

4.14

6.59

5.91

0.16

Correct answer:

6.59

Explanation:

To solve this, you need to set up a logarithm. Our exponent is . The number of which it is the exponent of (5) is the base. This is the logarithm's base. The value 40150 is the operand of the logarithm. Therefore, we can write an equation:

$\log_5 {40150} = t$

Now, you cannot do this on your calculator. Therefore, using the rule for converting logarithms, you need to change:

$\log_5 {40150}$

to...

$\frac{\log{40150}}{\log{5}}$

You can put this into your calculator and get:

6.58638499657496 , or rounded, 6.59

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Example Question #7 : Logarithms And Exponents

Write the equation $3^{-4}=\frac{1}{81}$ in logarithmic form.

Possible Answers:

$log_3\frac{1}{81}=-4$

$log_3{-4}=\frac{1}{81}$

$log_\frac{1}{81}3=-4$

$log_{-4}\frac{1}{81}=3$

$log_{-4}3=\frac{1}{81}$

Correct answer:

$log_3\frac{1}{81}=-4$

Explanation:

For logarithmic equations, a^c=b can be rewritten as log_ab=c .

In this expression, is the base of the equation (). is the exponent () and $\frac{1}{81}$ is the term ().

In putting each term in its appropriate spot, the exponential equation can be converted to $log_3\frac{1}{81}=-4$ .

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Example Question #8 : Logarithms And Exponents

Solve the following logarithm for :

log_5x=3

Possible Answers:

x=15

x=25

x=3

x=125

Correct answer:

x=125

Explanation:

Solve the following logarithm:

log_5x=3

Recall that we can convert logarithms to exponential form via the following:

log_ba=c b^c=a

Using this approach, convert the given log to exponential form:

5^3=x

x=125

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Example Question #4 : Exponential Functions

Rewrite the following expression as an exponential expression:

log_3b=14,000

Possible Answers:

14,000^3=b

$3^{14,000}=b$

$b^{14,000}=3$

b^3=14,000

Correct answer:

$3^{14,000}=b$

Explanation:

Rewrite the following expression as an exponential expression:

log_3b=14,000

Recall the following property of logs and exponents:

log_b(a)=c

Can be rewritten in the following form:

b^c=a

So, taking the log we are given;

log_3b=14,000

We can rewrite it in the form:

$3^{14,000}=b$

So b must be a really huge number!

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #41 : Logarithms

Example Question #2 : Exponential Functions

Example Question #3 : Exponential Functions

Example Question #42 : Understanding Logarithms

Example Question #3 : Logarithms And Exponents

Example Question #4 : Logarithms And Exponents

Example Question #1 : Logarithms And Exponents

Example Question #7 : Logarithms And Exponents

Example Question #8 : Logarithms And Exponents

Example Question #4 : Exponential Functions

All Algebra II Resources

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