Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the inverse of the function y=log_(3)x ?
(1) y=x^(3)
(2) y=log_(x)3
(3) y=3^(x)
(4) x=3^(y)

What is the inverse of the function $y=\log _{3} x$ ? $\newline$ (A) $y=x^{3}$ $\newline$ (B) $y=\log _{x} 3$ $\newline$ (C) $y=3^{x}$ $\newline$ (D) $x=3^{y}$

View step-by-step help

View step-by-step help

Quotient property of logarithms

Full solution

Q. What is the inverse of the function

y=\log _{3} x

?

\newline

(A)

y=x^{3}

\newline

(B)

y=\log _{x} 3

\newline

(C)

y=3^{x}

\newline

(D)

x=3^{y}

Identify Function Components: Identify the original function and its components. $\newline$ The original function is $y = \log_{3}(x)$ , which means that $3$ raised to the power of $y$ equals $x$ .
Write in Exponential Form: Write the original function in exponential form. $\newline$ To find the inverse, we switch $x$ and $y$ and solve for the new $y$ . So, we rewrite the equation as $x = 3^y$ .
Solve for Inverse Function: Solve for the new $y$ to express the inverse function. $\newline$ To express the inverse function, we solve for $y$ , which gives us $y = \log_{3}(x)$ . Since we have switched $x$ and $y$ , the inverse function is $x = 3^{y}$ .
Check Answer Choices: Check the answer choices to see which one matches the inverse function. $\newline$ The correct answer choice that matches $x = 3^y$ is ( $3$ ) $y = 3^{(x)}$ , since it represents the inverse relationship between $x$ and $y$ .

More problems from Quotient property of logarithms

Question

Write the exponential equation in logarithmic form.

\newline

9^3 = 729

\newline

\log_\square 729 = 3

Posted 2 months ago

Question

Write the exponential equation in logarithmic form.

\newline

e^4 \approx 54.598

\newline

\ln\_\_\_\_ \approx 4

Posted 2 months ago

Question

Write the logarithmic equation in exponential form.

\newline

\log_{10}100 = 2

\newline

10^2 = \underline{\hspace{2em}}

Posted 2 months ago

Question

Evaluate. Write your answer as a whole number, proper fraction, or improper fraction in simplest form.

\newline

\frac{\ln (e)}{10} =

Posted 2 months ago

Question

Rewrite as a quotient of two common logarithms. Write your answer in simplest form.

\newline

\log_3 33 =

Posted 2 months ago

Question

Evaluate. Round your answer to the nearest thousandth.

\newline

\log_{5}50 =

Posted 2 months ago

Question

Which property of logarithms does this equation demonstrate?

\newline

\log_3 3 + \log_3 6 = \log_3 18

\newline

\newline

\text{Product Property}

\newline

\text{Power Property}

\newline

\text{Quotient Property}

Posted 2 months ago

Question

Expand the logarithm. Assume all expressions exist and are well-defined.

\newline

Write your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.

\newline

\log(uv)

\newline

Posted 2 months ago

Question

Expand the logarithm. Assume all expressions exist and are well-defined.

\newline

Write your answer as a sum or difference of common logarithms or multiples of common logarithms. The inside of each logarithm must be a distinct constant or variable.

\newline

\log v^7

\newline

Posted 2 months ago

Question

Expand the logarithm. Assume all expressions exist and are well-defined.

\newline

Write your answer as a sum or difference of base-

6

logarithms or multiples of base-

6

logarithms. The inside of each logarithm must be a distinct constant or variable.

\newline

\log_6 w^6

\newline

Posted 2 months ago