Question

Using graphing, what are the approximate solutions to this equation? |2x-3|=log(2x-3)+2

Answer 1

The approximate solutions are: x = 1.505 and x = 2.688

Equation solutions

The solutions to an equation can be solved by graphing calculators and by solving them explicitly.

The equation is given as:

$|2x-3|=\log(2x-3)+2$

Start by splitting the given equation, as follows:

• $|2x-3|=0$,
• $\log(2x-3)+2 =0$

Rewrite the above equations as follows:

• $y = |2x-3|$.
• $y = \log(2x-3)+2$

The graphs

Plot the graphs of the above equations (see attachment).

From the graph, the equations intersect at the following points

• x = 1.505
• x = 2.688

Hence, the approximate solutions are: x = 1.505 and x = 2.688

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