Exponential and Logarithm Functions

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 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 base of the natural logarithm?

Back

The base of the natural logarithm is e, approximately equal to 2.71828.

Front

How do you convert a logarithmic equation to exponential form?

Back

To convert a logarithmic equation log_b(a) = c to exponential form, rewrite it as b^c = a.

Front

What is the product rule for logarithms?

Back

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

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What is the quotient rule for logarithms?

Back

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

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What is the power rule for logarithms?

Back

The power rule states that log_b(m^n) = n * log_b(m).

Front

What is continuous compounding in finance?

Back

Continuous compounding refers to the process of earning interest on an investment that is calculated and added to the principal continuously, rather than at discrete intervals.

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How do you calculate the time required for an investment to double with continuous compounding?

Back

The time required to double an investment with continuous compounding can be calculated using the formula t = ln(2) / r, where r is the annual interest rate.

Front

What is the value of ln(e^x)?

Back

ln(e^x) = x, because the natural logarithm and the exponential function are inverses.