Converting Logs to Exponents

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

Convert the logarithmic expression log_2(8) to exponential form.

Back

2^3 = 8.

Front

Evaluate log_10(1000).

Back

3, because 10^3 = 1000.

Front

What is the value of log_4(16)?

Back

2, because 4^2 = 16.

Front

If log_x(81) = 4, what is the value of x?

Back

3, because 3^4 = 81.

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

Evaluate log_5(25).

Back

2, because 5^2 = 25.

Front

What is the value of log_3(1)?

Back

0, because any number raised to the power of 0 equals 1.

Front

Convert log_6(36) = 2 to exponential form.

Back

6^2 = 36.

Front

If log_2(x) = 5, what is the value of x?

Back

32, because 2^5 = 32.