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

May 10, 2026Mathematics

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Answer

x = 2e^y

Graph of y = 1/2x

Key points of y = 1/2x
Point	x	y
x-intercept	0	0

3 steps

let's solve this equation for $x$ in terms of $y$ .

Given the equation:

y = \ln \left(\frac{1}{2}x\right)

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 $e$ .
$e^y = e^{\ln \left(\frac{1}{2}x\right)}$
Use the property that $e^{\ln A} = A$ .
$e^y = \frac{1}{2}x$
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 $\boxed{x = 2e^y}$ .