Evaluate Logarithms

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.

Tags

CCSS.HSF.BF.B.5

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, where k is the new base.

Front

What is the value of log_b(1) for any base b?

Back

The value of log_b(1) is always 0, because any number raised to the power of 0 equals 1.

Front

What is the value of log_b(b)?

Back

The value of log_b(b) is always 1, because any number raised to the power of 1 equals itself.

Front

How do you evaluate log_b(1/x)?

Back

log_b(1/x) = -log_b(x), which means the logarithm of the reciprocal is the negative of the logarithm.

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.

Tags

CCSS.HSF.BF.B.5

Front

What is the value of log_2(128)?

Back

The value of log_2(128) is 7, because 2^7 = 128.

Front

How do you evaluate log_7(1/49)?

Back

log_7(1/49) = log_7(49^{-1}) = -log_7(49) = -2, since 7^2 = 49.

Front

What is the value of log_4(1)?

Back

The value of log_4(1) is 0, because any base raised to the power of 0 equals 1.

Front

What is the value of log_6(1)?

Back

The value of log_6(1) is 0, because any base raised to the power of 0 equals 1.