Solving Basic Log Equations

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. For example, log_b(a) = c means b^c = a.

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.

Front

How do you solve the equation log_b(x) = c?

Back

To solve log_b(x) = c, rewrite it in exponential form: x = b^c.

Front

What is the value of log_2(16)?

Back

4, because 2^4 = 16.

Front

What is the value of log_8(64)?

Back

2, because 8^2 = 64.

Front

How do you solve log_2(x + 3) = 4?

Back

Rewrite in exponential form: x + 3 = 2^4, so x = 16 - 3 = 13.

Front

How do you solve log_8(4x + 4) = 2?

Back

Rewrite in exponential form: 4x + 4 = 8^2, so 4x = 64 - 4 = 60, thus x = 15.

Front

What is the solution to log_10(x) = 1?

Back

10, because 10^1 = 10.

Front

What is the solution to log_10(0.1)?

Back

-1, because 10^-1 = 0.1.

Front

What is the value of log_2(8)?

Back

3, because 2^3 = 8.