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Questions and Answers
Explain how the logarithmic property $ ext{log}_a(mn) = ext{log}_a m + ext{log}_a n$ can be applied to simplify $ ext{log}_3(27)$.
Explain how the logarithmic property $ ext{log}_a(mn) = ext{log}_a m + ext{log}_a n$ can be applied to simplify $ ext{log}_3(27)$.
$ ext{log}_3(27) = ext{log}_3(3 imes 9) = ext{log}_3(3) + ext{log}_3(9) = 1 + 2 = 3$
Using the property $ ext{log}_a rac{m}{n} = ext{log}_a m - ext{log}_a n$, determine how to solve $ ext{log}_5 rac{25}{5}$.
Using the property $ ext{log}_a rac{m}{n} = ext{log}_a m - ext{log}_a n$, determine how to solve $ ext{log}_5 rac{25}{5}$.
$ ext{log}_5 rac{25}{5} = ext{log}_5(25) - ext{log}_5(5) = 2 - 1 = 1$
Illustrate how to apply the rule $ ext{log}_a(m^n) = n ext{log}_a m$ to calculate $ ext{log}_2(64)$.
Illustrate how to apply the rule $ ext{log}_a(m^n) = n ext{log}_a m$ to calculate $ ext{log}_2(64)$.
$ ext{log}_2(64) = ext{log}_2(2^6) = 6 imes ext{log}_2(2) = 6 \ (\text{since } \text{log}_2(2) = 1)$
Apply the logarithm property $ ext{log}a 1 = 0$ and evaluate $ ext{log}{10}( rac{100}{100})$.
Apply the logarithm property $ ext{log}a 1 = 0$ and evaluate $ ext{log}{10}( rac{100}{100})$.
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Using the property $ ext{log}a y = y$, derive the value of $ ext{log}{10}10$.
Using the property $ ext{log}a y = y$, derive the value of $ ext{log}{10}10$.
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Flashcards
Log Rule 1
Log Rule 1
The logarithm of a product is equal to the sum of the logarithms of the factors.
Log Rule 2
Log Rule 2
The logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator.
Log Rule 3
Log Rule 3
The logarithm of a power is equal to the exponent times the logarithm of the base.
Log of 1
Log of 1
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Log of Base
Log of Base
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