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Exponents and Logarithmic Equations Reviewer

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Questions and Answers

Which of the following represents the equation for exponential growth?

$y = rac{1}{2^x}$

$y = 2^x$ (correct)

$y = x^2$

$y = rac{1}{x}$

What is the result of $2^3$?

$6$

$16$

$8$ (correct)

$5$

What is the inverse function of $y = rac{1}{3} imes 2^x$?

$y = 2 imes log_3(x)$

$y = rac{log_2(x)}{3}$ (correct)

$y = rac{1}{3} imes log_2(x)$

$y = 3 imes log_2(x)$

What is the solution to the equation $log_2(x) = 4$?

$x = 16$ Signup and view all the answers

What is the result of $5^3$?

$125$ Signup and view all the answers

Which of the following is a property of logarithms?

$log_b(1) = 0$ Signup and view all the answers

What is the solution to the equation $2^{x+1} = 16$?

$x = 4$ Signup and view all the answers

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.