2. Graphically solve the equation $\log _{2}(x-1)+1=-\frac{3}{2} x+4$. Verify the solution by calculation.
2. We draw the logarithmic function $f$ with the rule $f(x)=\log _{2}(x-1)+1$ and the linear function $g$ with the rule $g(x)=-\frac{3}{2} x+4$. We read the solution $x=2$ and verify it computationally.

![](https://cdn.mathpix.com/cropped/2024_06_07_97c791425a4f6cf5fca5g-11.jpg?height=629&width=625&top_left_y=1099&top_left_x=721)

Graph of the logarithmic function........................................................................

Graph of the linear function.................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_97c791425a4f6cf5fca5g-11.jpg?height=52&width=1642&top_left_y=1867&top_left_x=207)

Verification........................................................................................................

