Exponential & Logarithmic Functions

Front

What is the logarithmic form of the equation 3^4 = 81?

Back

log_3(81) = 4

Front

How do you solve the equation log_6(3x - 2) = log_6(5x - 8) for x?

Back

x = 3

Front

What is the natural logarithm of a number?

Back

The natural logarithm (ln) is the logarithm to the base e, where e is approximately equal to 2.71828.

Front

How do you solve the equation 5 ln(3x - 2) = 15 for x?

Back

x = 7.36

Front

What is the inverse of the function f(x) = -4x - 12?

Back

f^(-1)(x) = -1/4x - 3

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.

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 relationship between exponential and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other. If y = b^x, then x = log_b(y).

Front

What is the value of log_10(1000)?

Back

log_10(1000) = 3, because 10^3 = 1000.

Front

How do you express log_b(mn) in terms of logarithms of m and n?

Back

log_b(mn) = log_b(m) + log_b(n).