Approximating the Solution of a Logarithmic Equation

Press [Y=] and enter $4\ln \left(x\right)+1$ next to Y₁=. Then enter $-2\ln \left(x-1\right)$ next to Y₂=. For a window, use the values 0 to 5 for $x$ and –10 to 10 for $y.$ Press [GRAPH]. The graphs should intersect somewhere a little to right of $x=1.$

For a better approximation, press [2ND] then [CALC]. Select [5: intersect] and press [ENTER] three times. The x-coordinate of the point of intersection is displayed as 1.3385297. (Your answer may be different if you use a different window or use a different value for Guess?) So, to the nearest thousandth, $x\approx \mathrm{1.339.}$