Exponential and Logarithmic Forms

Front

What is the definition of an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What is the definition of a logarithm?

Back

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

Front

What is the relationship between exponential and logarithmic forms?

Back

The relationship is defined by the equation: if b^y = x, then log_b(x) = y.

Front

Convert the exponential equation 2^3 = 8 into logarithmic form.

Back

log_2(8) = 3.

Front

Convert the logarithmic equation log_5(25) = 2 into exponential form.

Back

5^2 = 25.

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

If log_10(100) = 2, what is the equivalent exponential form?

Back

10^2 = 100.

Front

What is the value of log_3(81)?

Back

4, because 3^4 = 81.

Front

What is the value of log_2(32)?

Back

5, because 2^5 = 32.

Front

What is the value of log_36(1)?

Back

0, because 36^0 = 1.