Logarithmic functions

Graphs of Logaritmic and Exponential functions

Submitted by michaela.bailova on Fri, 04/19/2024 - 14:54

2010016010

Level:

Given the function

f (x) = \log_{2} (x + 4)

, evaluate

f (4) \cdot f (12)

12

48

128

4

2010016009

Level:

Given the function

f (x) = \log_{2} (x^{2} + 4)

, evaluate

f (2) \cdot f (0)

6

32

0

24

2010016006

Level:

Let

a = \log_{4} \frac{1}{64}

;

b = \log_{4} 4

and

c = \log_{4} \frac{1}{16}

. Which of the following statements is true?

a < c < b

b < c < a

c < b < a

a < b < c

2010016005

Level:

Let

a = \log_{3} \frac{1}{9}

;

b = \log_{3} 3

and

c = \log_{3} \frac{1}{27}

. Which of the following statements is true?

c < a < b

c < b < a

b < c < a

a < c < b

2000014109

Level:

Identify which of the following relations is correct.

\log_{3} 10 > 2

\log_{2} 7 > 3

\log_{2} 3 < \log_{3} 2

\log_{4} 15 > 2

2000014102

Level:

Make a true statement: The number

(\log_{6} 3)^{2} + (\log_{6} 2)^{2} + \log_{6} 4 \cdot \log_{6} 3

positive.

smaller than 1.

negative.

irrational.

2000014101

Level:

Find the domain of the function

f (x) = \log_{2015} (\log_{\frac{1}{2015}} (\log_{2015} x))

(1; 2015)

(2015; \infty)

(0; \infty)

(0; 2015)

2010011009

Level:

Identify which of the following relations is correct. Use the graph of

f (x) = \log_{\frac{1}{3}} x

given below.

\log_{\frac{1}{3}} 8 < \log_{\frac{1}{3}} 4 < \log_{\frac{1}{3}} 1 < \log_{\frac{1}{3}} \frac{1}{2} < \log_{\frac{1}{3}} \frac{1}{5}

\log_{\frac{1}{3}} \frac{1}{5} < \log_{\frac{1}{3}} \frac{1}{2} < \log_{\frac{1}{3}} 1 < \log_{\frac{1}{3}} 4 < \log_{\frac{1}{3}} 8

\log_{\frac{1}{3}} \frac{1}{2} < \log_{\frac{1}{3}} \frac{1}{5} < \log_{\frac{1}{3}} 1 < \log_{\frac{1}{3}} 4 < \log_{\frac{1}{3}} 8

\log_{\frac{1}{3}} 8 < \log_{\frac{1}{3}} 4 < \log_{\frac{1}{3}} 1 < \log_{\frac{1}{3}} \frac{1}{5} < \log_{\frac{1}{3}} \frac{1}{2}

2010011008

Level:

In the following list identify a positive expression.

\log_{0.5} 3 - \log_{0.5} 48

\log_{0.5} 16 + \log_{0.5} 4

\log_{3} 9^{3} - \log_{2} 4^{4}

\log_{5} (4^{- 1}) + \log_{5} \frac{4}{125}

Graphs of Logaritmic and Exponential functions

2010016010

2010016009

2010016006

2010016005

2000014109

2000014102

2000014101

2010011009

2010011008

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