logarithm textbook questions ap state
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The laws of logarithms help to solve complex calculations:
Logarithm of a product (Product Law): Logarithm of two or more positive numbers to any real base (Greater than 1) is equal to the sum of their logarithms to the same base.
logx ab = logx a + logx b
Logarithm of a quotient (Quotient Law): Logarithm of the quotient of any two positive numbers to any real base (Greater than 1) is equal to the logarithm of the numerator minus the logarithm of the denominator to the same base.
logx ( a b ) = logx a - logx b
Logarithm of a power (Power Law): Logarithm of a number raised to any rational index, to any real base (Greater than 1) is equal to the product of the index and the logarithm of the given number to the same base.
logx am = mlogx a
The laws of logarithms help to solve complex calculations:
Logarithm of a product (Product Law): Logarithm of two or more positive numbers to any real base (Greater than 1) is equal to the sum of their logarithms to the same base.
logx ab = logx a + logx b
Logarithm of a quotient (Quotient Law): Logarithm of the quotient of any two positive numbers to any real base (Greater than 1) is equal to the logarithm of the numerator minus the logarithm of the denominator to the same base.
logx ( a b ) = logx a - logx b
Logarithm of a power (Power Law): Logarithm of a number raised to any rational index, to any real base (Greater than 1) is equal to the product of the index and the logarithm of the given number to the same base.
logx am = mlogx a
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