Exponential and Logarithm Review

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, leading to rapid increases as the quantity grows.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to rapid decreases as the quantity shrinks.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a * b^x, where 'a' is the initial value, 'b' is the growth (b > 1) or decay (0 < b < 1) factor, and 'x' is the exponent.

Front

What is a logarithm?

Back

A logarithm is the inverse operation to exponentiation, answering the question: to what exponent must a base be raised to produce a given number.

Front

What is the relationship between exponents and logarithms?

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If b^y = x, then log_b(x) = y. This means that logarithms can be used to solve for exponents.

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What is the base of a logarithm?

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The base of a logarithm is the number that is raised to a power to obtain another number. Common bases are 10 (common logarithm) and e (natural logarithm).

Front

What is the product rule of logarithms?

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The product rule states that log_b(M * N) = log_b(M) + log_b(N), allowing the logarithm of a product to be expressed as the sum of logarithms.

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What is the quotient rule of logarithms?

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The quotient rule states that log_b(M / N) = log_b(M) - log_b(N), allowing the logarithm of a quotient to be expressed as the difference of logarithms.

Front

What is the power rule of logarithms?

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The power rule states that log_b(M^p) = p * log_b(M), allowing the logarithm of a power to be expressed as a product.

Front

How do you solve an exponential equation?

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To solve an exponential equation, you can take the logarithm of both sides to bring down the exponent and then solve for the variable.