3.4 Practice: Solving Exp & Logs using Inverses

Front

What is the inverse operation of exponentiation?

Back

Logarithm

Front

When do you need to take the logarithm of both sides of an equation?

Back

When the variable is in the exponent.

Front

What is the base of the natural logarithm?

Back

e (approximately 2.718) is the base of the natural logarithm.

Front

What is the change of base formula for logarithms?

Back

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

Front

What is the product property of logarithms?

Back

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

Front

What is the quotient property of logarithms?

Back

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

Front

What is the power property of logarithms?

Back

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

Front

How do you solve the equation 3^(2x - 6) = 81?

Back

x = 5.

Front

What is the solution to log_2(2) + log_2(8x) = 6?

Back

x = 4.

Front

How do you solve log(x) - log(8) = 3?

Back

x = 8000.