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Popular Algebra >

solvefor x,e^{x/2}=4lnx

  • Pre Algebra
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Solution

solve for x,e2x​=4ln(x)

Solution

x≈1.92309,2.89429
Solution steps
e2x​=4ln(x)
Find the difference functionf(x)=e2x​−4ln(x)
Look for the function's extreme points
Extreme Points of e2x​−4ln(x),x>0:Minimum(2.40433…,−0.18177…)
Check function behavior at domain edges: 0,∞
x→0+lim​(e2x​−4ln(x))=∞
x→∞lim​(e2x​−4ln(x))=∞
The interval between every consecutive point pair is monotone
xf(x)​0∞​2.40433…−0.18177…​∞∞​​
Check every interval, if the signs at the edges are different, find the X intersection using Brent method
Between (0,∞) and (2.40433…,−0.18177…)1.92309
Between (2.40433…,−0.18177…) and (∞,∞)2.89429
x≈1.92309,2.89429

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Popular Examples

2^{-b}=15^{5-x}= 1/25solvefor x,3125^{x+4}=25^{2x}7^y=153^{2x}-3(3^x)=4

Frequently Asked Questions (FAQ)

  • What is the answer to solvefor x,e^{x/2}=4lnx ?

    The answer to solvefor x,e^{x/2}=4lnx is x\approx 1.92309,2.89429

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