Solve Exponential Equations

Front

What is an exponential equation?

Back

An equation in which a variable appears in the exponent, such as a^x = b.

Front

How do you solve the equation 7^(-x) = 49?

Back

x = -2, because 49 can be rewritten as 7^2.

Front

What is the change of base formula for logarithms?

Back

log_b(a) = log_k(a) / log_k(b), where k is any positive number.

Front

How do you evaluate log(17/6)?

Back

Use the change of base formula: log(17/6) = log(17) - log(6).

Front

What is the solution to the equation 8 = 2^(5x + 7)?

Back

x = -4/5.

Front

If 3^3 = 3^(4x + 2), what is x?

Back

x = 1/4.

Front

What does it mean for two exponential expressions to be equal?

Back

Their bases must be the same, or their exponents must be equal if the bases are different.

Front

How do you convert an exponential equation to a logarithmic form?

Back

If a^b = c, then log_a(c) = b.

Front

What is the value of log_6(36)?

Back

log_6(36) = 2, because 6^2 = 36.

Front

What is the relationship between exponential and logarithmic functions?

Back

Logarithmic functions are the inverses of exponential functions.