Warmup: Exponential Equations & Evaluating Logarithms

Front

What is an exponential equation?

Back

An exponential equation is an equation in which a variable appears in the exponent. For example, in the equation 3^(x+1) = 27, the variable x is in the exponent.

Front

How do you solve the exponential equation 3^(x+1) = 27?

Back

To solve 3^(x+1) = 27, rewrite 27 as 3^3. This gives 3^(x+1) = 3^3. Since the bases are the same, set the exponents equal: x + 1 = 3. Solving this gives x = 2.

Front

What is the logarithmic form of the equation 3^4 = 81?

Back

The logarithmic form of the equation 3^4 = 81 is log_3(81) = 4.

Front

How do you evaluate log_3(1/3)?

Back

To evaluate log_3(1/3), recognize that 1/3 can be rewritten as 3^(-1). Therefore, log_3(1/3) = log_3(3^(-1)) = -1.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms are the inverse operations of exponentiation. If b^y = x, then log_b(x) = y.

Front

How do you convert log_6(36) = 2 to exponential form?

Back

To convert log_6(36) = 2 to exponential form, rewrite it as 6^2 = 36.

Front

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain a given number. In log_b(x), b is the base.

Front

What is the value of log_3(3)?

Back

The value of log_3(3) is 1, because 3^1 = 3.

Front

What is the value of log_3(9)?

Back

The value of log_3(9) is 2, because 3^2 = 9.

Front

What is the change of base formula for logarithms?

Back

The change of base formula states that log_b(a) = log_k(a) / log_k(b) for any positive k.