How to solve for x
x = 1.5 ln(x) + 2.5
#Algebra/Calculus Question
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How to solve for x
x = 1.5 ln(x) + 2.5
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dense dune
Plug it in geogebra. I don't think it can be solved analytically.
Actually lets consider the function f(x)=1.5lnx+2.5-x, x>0 Find the intervals where the derivative preserves its sign you will find that for 0<x<1.5 f'(x)>0 → f strictly increasing and for x>1.5 f'(x)<0 f strictly decreasing. Find the value f(1.5) which is the global maximum of f.
Now if f(1.5)<0 then that would mean your equation has no solutions.
Unfortunately that is not the case and f(1.5)>0
There could be up to two solutions one before x=1.5 and one after x=1.5
Now you could apply some numerical method to solve this equation. Like Newton's method, or bisection method. Google those.
Bisection method might work better because you know the intervals where the two solutions might lie.