Logarithms (easy)

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, if b^y = x, then log_b(x) = y.

Front

Convert the exponential equation 2^3 = 8 into logarithmic form.

Back

log_2(8) = 3.

Front

What is the value of log_10(100)?

Back

2, because 10^2 = 100.

Front

What is the value of log_4(1)?

Back

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

Front

Rewrite the logarithmic equation log_3(27) = x in exponential form.

Back

3^x = 27.

Front

If log_b(x) = y, what is the equivalent exponential form?

Back

b^y = x.

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_2(16)?

Back

4, because 2^4 = 16.

Front

If log_8(x) = 2, what is the value of x?

Back

64, because 8^2 = 64.