Solving Logarithmic Equations

Front

What is the product rule of logarithms?

Back

log_b(MN) = log_b(M) + log_b(N) for any positive numbers M and N.

Front

What is the quotient rule of logarithms?

Back

log_b(M/N) = log_b(M) - log_b(N) for any positive numbers M and N.

Front

What is the power rule of logarithms?

Back

log_b(M^p) = p * log_b(M) for any positive number M and real number p.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b) for any positive number k.

Front

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

Back

x = 2.

Front

Solve: log_2(x+3) = 4

Back

x = 13.

Front

What is the natural logarithm?

Back

The natural logarithm is the logarithm to the base e, denoted as ln(x).

Front

What is the common logarithm?

Back

The common logarithm is the logarithm to the base 10, denoted as log(x).

Front

If log_b(x) = y, what is the equivalent exponential form?

Back

b^y = x.

Front

Solve: log_5(4x-7) = log_5(x+5)

Back

x = 4.