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Logarithmic functions and exponential functions are __________ functions. The product property of exponents...

Logarithmic functions and exponential functions are __________ functions.
The product property of exponents states that b^m * b^n = b^(m+n), so multiplying powers with the same base means the exponents are __________.
The product property of logarithms states that log_b(MN) = log_b(M) + log_b(N), so the logarithm of a product can be rewritten as a __________.
The quotient property of exponents states that b^m / b^n = b^(m-n), so dividing powers with the same base means the exponents are __________.
The quotient property of logarithms states that log_b(M/N) = log_b(M) - log_b(N), so the logarithm of a quotient can be rewritten as a __________.

Answer

  1. Logarithmic functions and exponential functions are inverse functions.

  2. The product property of exponents states that b^m * b^n = b^(m+n), so multiplying powers with the same base means the exponents are added.

  3. The product property of logarithms states that log_b(MN) = log_b(M) + log_b(N), so the logarithm of a product can be rewritten as a sum.

  4. The quotient property of exponents states that b^m / b^n = b^(m-n), so dividing powers with the same base means the exponents are subtracted.

  5. The quotient property of logarithms states that log_b(M/N) = log_b(M) - log_b(N), so the logarithm of a quotient can be rewritten as a difference.

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