radical x = 1+ln(5+x)

Question

Logrithms. I need to solve for x

Answer 1

I assume this is √x=1+ln(5+x).

I would use Newton's Method (iterative): x_n+1=x_n-f(x_n)/f'(x_n),

where f(x)=1+ln(5+x)-√x and f'(x)=1/(5+x)-1/(2√x).

Let x₀=1, then x₁=1-ln(6)/(⅙-½)=1+ln(6)/3=6.375...,

After just a few iterations x=16.5788535284.