Rewriting Exponentials

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, which means b^c = a.

Front

How do you convert a logarithmic equation to exponential form?

Back

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

Front

What is the base in a logarithmic expression?

Back

The base in a logarithmic expression log_b(a) is the number b that is raised to the power c to obtain a.

Front

What is the relationship between logarithms and exponents?

Back

Logarithms and exponents are inverse operations. If b^c = a, then log_b(a) = c.

Front

What is the exponential form of log_2(8) = 3?

Back

The exponential form is 2^3 = 8.

Front

Rewrite log_3(81) = 4 in exponential form.

Back

The exponential form is 3^4 = 81.

Front

What is the exponential form of log_v(n) = a?

Back

The exponential form is v^a = n.

Front

How do you express log_6(t) = m in exponential form?

Back

The exponential form is 6^m = t.

Front

What is the value of log_10(100) in terms of exponents?

Back

log_10(100) = 2, because 10^2 = 100.

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.