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Logarithmic Functions Practice Flashcards

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Logarithmic Functions Practice Flashcards

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Questions and Answers

Write the equation in logarithmic form: 625=5^4

Log5 625=4

Write the equation in logarithmic form: (1/3)^3?

Log(1/3)^3=1/27

Write the equation in exponential form: Log2 128=7?

128=2^7

Write the equation in exponential form: Log3 1/9=-2?

1/9=3^-2 Signup and view all the answers

Evaluate the logarithm: Log2 16?

4 Signup and view all the answers

Evaluate the logarithm: Log49 7?

1/2 Signup and view all the answers

Evaluate the logarithm: Log5 (-25)?

Undefined Signup and view all the answers

Evaluate the logarithm: Log5 1?

0 Signup and view all the answers

Describe how the graph of each function compares with the graph of the parent function y=log5 x+1?

It translates the graph up 1 unit Signup and view all the answers

Describe how the graph of each function compares with the graph of the parent function y=log3 (x-5)+3?

Translate the graph to the right 5 units and up to 3 units Signup and view all the answers

Study Notes

Logarithmic Function as Inverses

Logarithmic Form of 625 = 5^4:
Logarithmic equation expressed as Log₅ 625 = 4.
Logarithmic Form of (1/3)³ = 1/27:
Written as Log(1/3) 1/27 = 3.
Exponential Form of Log₂ 128 = 7:
Converted to exponential form gives 128 = 2^7.
Exponential Form of Log₃ (1/9) = -2:
Translates to 1/9 = 3^(-2).
Evaluation of Log₂ 16:
The value of Log₂ 16 is 4, since 2^4 = 16.
Evaluation of Log₄₉ 7:
The result of Log₄₉ 7 is 1/2, as 49^(1/2) = 7.
Value of Log₅ (-25):
Logarithm of a negative number is undefined.
Evaluation of Log₅ 1:
The value is 0 because any number raised to the power of 0 equals 1.

Graph Comparisons

Graph of y = log₅ x + 1:
This function translates the parent graph y = log₅ x upward by 1 unit.
Graph of y = log₃ (x - 5) + 3:
This function shifts the parent graph right by 5 units and up by 3 units.

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Description

Test your understanding of logarithmic functions and their inverses with these flashcards. Practice converting between exponential and logarithmic forms to enhance your math skills and confidence. Ideal for students learning about logarithmic equations.