Logarithmic and Exponential Equations

Front

What is the definition of a logarithm?

Back

A logarithm is the power to which a number (the base) must be raised to obtain another number. For example, log_b(a) = c means b^c = a.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions can be rewritten in logarithmic form. For example, if b^y = x, then log_b(x) = y.

Front

How do you convert an exponential equation to logarithmic form?

Back

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

Front

What is the value of log_3(81)?

Back

4, because 3^4 = 81.

Front

How do you solve for x in the equation 2^x = 8?

Back

x = 3, because 2^3 = 8.

Front

What is the logarithmic form of the equation 6^x = 64?

Back

log_6(64) = x.

Front

What is the value of log_9(3)?

Back

1/2, because 9^(1/2) = 3.

Front

How do you solve the equation 6^3 ⋅ 6^w = 36 for w?

Back

w = -1.

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

What is the definition of the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately 2.718.