Let f(x)=4x-ln(7x+15)=0, then we can use Newton's Method to solve this iteratively:
xn+1=xn-f(xn)/f'(xn) where xn is the nth iteration of x, and f'(x)=df/dx.
f'(x)=df/dx=4-7/(7x+15)
We need a starting value for x (x0), so let x0=0.
f(0)=-ln(15); f'(0)=4-7/15=53/15.
x1=ln(15)/(4-7/15)=15ln(15)/53=0.766429 approx.
x2=0.752235,
x3=0.752231,
x4=0.752231. To 6 decimal places x=0.752231.