Solving Exponential and Logarithmic Equations Flashcard

Front

What is the product property of logarithms?

Back

The product property states that log_b(MN) = log_b(M) + log_b(N), where M and N are positive numbers.

Front

What is the quotient property of logarithms?

Back

The quotient property states that log_b(M/N) = log_b(M) - log_b(N), where M and N are positive numbers.

Front

What is the power property of logarithms?

Back

The power property states that log_b(M^p) = p * log_b(M), where M is a positive number and p is any real number.

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.

Front

What is the definition of a logarithm?

Back

A logarithm is the exponent to which a base must be raised to produce a given number. For example, if b^y = x, then log_b(x) = y.

Front

Solve: log(x) + log(x+3) = 1

Back

x = 2

Front

Solve: ln(x+8) - ln(8) = 3

Back

x = 152.68

Front

Determine the correct set-up for: log_4(x-1) - log_4(x+7) = log_4(6)

Back

log_4((x-1)/(x+7)) = log_4(6)

Front

Solve: 2(16^(x+6)) - 8 = 35

Back

x = -4.89

Front

Solve: log_5(-60+n) = log_5(n^2+17n)

Back

No Solution