4.2 Convert and Evaluate Logs

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. It is expressed as log_b(a) = c, meaning b^c = a.

Front

What is the relationship between logarithms and exponents?

Back

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

Front

How do you convert a logarithmic equation to an exponential equation?

Back

To convert log_b(a) = c to exponential form, rewrite it as b^c = a.

Front

What is the base of a logarithm when no base is specified?

Back

When no base is specified, the base of the logarithm is assumed to be 10 (common logarithm).

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 log₄(16)?

Back

To evaluate log₄(16), recognize that 4² = 16, so log₄(16) = 2.

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 base k.

Front

How do you express y = 7^x in logarithmic form?

Back

To express y = 7^x in logarithmic form, write log₇(y) = x.

Front

What is the value of log₇(7⁰)?

Back

The value of log₇(7⁰) is 0, because 7 raised to the power of 0 equals 1.