Rewriting log and exponential equations

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. For example, log_b(a) = c means b^c = a.

Front

Rewrite the exponential equation 4^x = 64 in logarithmic form.

Back

log_4(64) = x.

Front

What is the base of the logarithm in the equation log_4(1/64) = -3?

Back

The base is 4.

Front

How do you express the equation 2^5 = 32 in logarithmic form?

Back

log_2(32) = 5.

Front

What is the relationship between exponential and logarithmic functions?

Back

Exponential functions are the inverse of logarithmic functions.

Front

If log_b(a) = c, what is the equivalent exponential form?

Back

b^c = a.

Front

What is the value of log_10(1000)?

Back

3, because 10^3 = 1000.

Front

How do you rewrite the equation 3^x = 1/27 in logarithmic form?

Back

log_3(1/27) = x.

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 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 the base, and x is the exponent.