Logarithm to Exponential and Vice Versa

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

How do you convert an exponential equation to logarithmic form?

Back

To convert an exponential equation of the form b^c = a to logarithmic form, you write it as log_b(a) = c.

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

What is the base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power. In log_b(a), b is the base.

Front

How do you rewrite log_b(a) in exponential form?

Back

To rewrite log_b(a) in exponential form, you express it as b^c = a, where c is the logarithm.

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

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 is itself.

Front

What is the value of log_b(1)?

Back

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

Front

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

Back

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

Front

What is the logarithmic form of 10^3 = 1000?

Back

The logarithmic form is log_10(1000) = 3.