exponential and logarithm review

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 base of a logarithm?

Back

The base of a logarithm is the number that is raised to a power to obtain another number. For example, in log_b(a) = c, b is the base.

Front

What is the relationship between exponents and logarithms?

Back

Logarithms are the inverse operations of exponentiation. If b^c = a, then log_b(a) = c.

Front

How do you condense logarithmic expressions?

Back

To condense logarithmic expressions, use the properties of logarithms, such as log_b(m) + log_b(n) = log_b(m*n) and log_b(m) - log_b(n) = log_b(m/n).

Front

Expand the logarithmic expression: log_b(m^n).

Back

The expansion is n * log_b(m).

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

Solve the equation: 2^(x+6) = 32. What is x?

Back

x = -1.

Front

What is the value of log_10(1000)?

Back

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

Front

What is the product rule for logarithms?

Back

The product rule states that log_b(m*n) = log_b(m) + log_b(n).

Front

What is the quotient rule for logarithms?

Back

The quotient rule states that log_b(m/n) = log_b(m) - log_b(n).