Solving Exponential Equations: Rewriting Bases and Using Logs

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 exponential equations with the same base?

Back

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

Front

What is the logarithm of a number?

Back

The exponent to which a base must be raised to produce that number.

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

How do you rewrite 10^(x-3) = 10^(8x-10)?

Back

Set the exponents equal: x - 3 = 8x - 10.

Front

What is the solution to the equation 10^(x-3) = 10^(8x-10)?

Back

x = 1.

Front

How do you solve 9e^x - 31 = 23?

Back

Isolate e^x and take the natural logarithm.

Front

What is the solution to 9e^x - 31 = 23?

Back

x = 1.79.

Front

How do you rewrite 36 = 6^x?

Back

Rewrite 36 as 6^2.

Front

What is the solution to 36 = 6^x?

Back

x = 2.