Solving Exponential Equations (using logs)

Front

What is an exponential equation?

Back

An equation in which a variable appears in the exponent, typically in the form of a^x = b.

Front

How do you solve an exponential equation using logarithms?

Back

Take the logarithm of both sides of the equation to bring down the exponent, then solve for the variable.

Front

What is the logarithmic form of the equation a^x = b?

Back

x = log_a(b), where log_a is the logarithm base a.

Front

What is the change of base formula for logarithms?

Back

log_a(b) = log_c(b) / log_c(a) for any positive c.

Front

What is the value of log_10(100)?

Back

2, because 10^2 = 100.

Front

What is the value of log_2(8)?

Back

3, because 2^3 = 8.

Front

If 2^x = 16, what is x?

Back

4, because 2^4 = 16.

Front

If 3^x = 1/27, what is x?

Back

-3, because 3^(-3) = 1/27.

Front

What is the natural logarithm of e (ln(e))?

Back

1, because e^1 = e.

Front

What is the property of logarithms: log_a(mn)?

Back

log_a(m) + log_a(n), the logarithm of a product is the sum of the logarithms.