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Questions and Answers
Which of the following represents the equation for exponential growth?
What is the result of $2^3$?
What is the inverse function of $y = rac{1}{3} imes 2^x$?
What is the solution to the equation $log_2(x) = 4$?
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What is the result of $5^3$?
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Which of the following is a property of logarithms?
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What is the solution to the equation $2^{x+1} = 16$?
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Study Notes
Exponential Growth and Logarithms
- The equation for exponential growth is not explicitly stated, but it can be represented as $y = ab^x$, where $a$ is the initial value, $b$ is the growth factor, and $x$ is the time period.
- The result of $2^3$ is 8, which is an example of exponential growth.
Exponential Functions
- The inverse function of $y = \frac{1}{3} \times 2^x$ is $x = log_2(3y)$, which is a logarithmic function.
Logarithms
- The solution to the equation $log_2(x) = 4$ is $x = 2^4 = 16$, which is an example of a logarithmic equation.
- The result of $5^3$ is 125, which is an example of exponential growth.
Properties of Logarithms
- One property of logarithms is that $log_a(x) = y \iff a^y = x$, which is a fundamental property of logarithms.
Exponential Equations
- The solution to the equation $2^{x+1} = 16$ can be found by noticing that $2^4 = 16$, so $x+1 = 4$, which implies that $x = 3$, which is the solution to the equation.
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Description
Prepare for your exam by reviewing the Law of Exponents, exponents equations (functions), law of logs, and logarithmic equations (functions) with this comprehensive quiz.
