Sketch the graph of $y={{2}^{x}}$. In order to solve the equation \(\frac{1}{2}x={{\log }_{2}}\sqr

Question

Sketch the graph of $y={{2}^{x}}$. In order to solve the equation $\frac{1}{2}x={{\log }_{2}}\sqrt{3-2x}$, a suitable straight line has to be drawn on the same diagram as the graph of $y={{2}^{x}}$. Find the equation of the straight line and the number of solutions to the equation.

Accepted Answer

Both equations have one real solution. Suitable lines: $y=-2x+3$ and $y=x-3$.

Solving Equation Graphically

Solving Equation Graphically

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