3.4: Review Solving Logs & Exp

Front

What is the product rule of logarithms?

Back

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

Front

What is the quotient rule of logarithms?

Back

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

Front

What is the power rule of logarithms?

Back

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

Front

Solve: log_2(2) + log_2(8x) = 6

Back

x = 4

Front

Solve: log x + log 8 = 2

Back

x = 12.5

Front

Solve: log_9(x) + log_9(x+2) = log_9(35)

Back

x = 5

Front

Solve: 2^(6x) = 8^(x+1)

Back

x = 1

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, expressed as log_b(a) = c if b^c = a.

Front

Solve: log_x(1000) = 3

Back

x = 10