Solve for x in terms of y: y = ((1)/(2)x)

May 10, 2026Mathematics

ScanSolve AI Answer

May 10, 2026

Answer

$x = 2e^y$

You're on a roll — let's solve this equation for $x$ in terms of $y$ .

Given the equation: $y = \ln \left(\frac{1}{2}x\right)$

Step 1: To isolate the term containing $x$ , we need to remove the natural logarithm ( $\ln$ ). We do this by exponentiating both sides of the equation with base $e$ . $e^y = e^{\ln \left(\frac{1}{2}x\right)}$

Step 2: Use the property that $e^{\ln A} = A$ . $e^y = \frac{1}{2}x$

Step 3: To solve for $x$ , multiply both sides of the equation by 2. $2 \cdot e^y = 2 \cdot \frac{1}{2}x$ $2e^y = x$

The solution for $x$ in terms of $y$ is $\boxed{x = 2e^y}$ .

Send me the next one 📸

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp

More Mathematics Questions

Q2 Find the value of x if 3x+4=19. 3 Find the value of y when 2y-7=21.QA teacher chooses 3 pens. The teacher randomly guesses a pen to use on an assignment. He, he will ke…QA. Write an equation and solve it. 1. Six times a certain number decreased by two is four times the…QWhen a certain number is increased by five, the result is six times the same number decreased by ten…QNumeric and geometric patterns. 1. Determine the constant difference or the constant ratio of the fo…

See all Mathematics questions →

Still have questions?

Quick Answer

You're on a roll — let's solve this equation for x in terms of y. Given the equation: y = ((1)/(2)x) Step 1: To isolate the term containing x, we need to remove the natural logarithm ().

Asked on May 10, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 10, 2026

You're on a roll — let's solve this equation for x in terms of y. Given the equation: y = ((1)/(2)x) Step 1: To isolate the term containing x, we need to remove the natural logarithm (). We do this by exponentiating both sides of the equation with base e. e^y = e^ ((1)/(2)x) Step 2: Use the property that e^ A = A. e^y = (1)/(2)x Step 3: To solve for x, multiply both sides of the equation by 2. 2 · e^y = 2 · (1)/(2)x 2e^y = x The solution for x in terms of y is x = 2e^y. Send me the next one 📸