Warm Up: Solving Exponential (same base) & Log Equations

Front

What is the property of exponents that allows us to set the exponents equal to each other when the bases are the same?

Back

If a^m = a^n, then m = n, provided a > 0 and a ≠ 1.

Front

How do you solve an exponential equation with the same base?

Back

Set the exponents equal to each other and solve for the variable.

Front

What is the logarithmic form of the equation 5^x = y?

Back

x = log_5(y).

Front

What is the change of base formula for logarithms?

Back

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.

Front

How do you solve log equations with the same base?

Back

Set the arguments equal to each other and solve for the variable.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions are the inverse of logarithmic functions.

Front

What is the value of log_b(b)?

Back

log_b(b) = 1.

Front

What is the value of log_b(1)?

Back

log_b(1) = 0.

Front

How do you simplify log_b(mn)?

Back

log_b(mn) = log_b(m) + log_b(n).