Using a Graph to Understand the Solution to a Logarithmic Equation

Solve $\ln x = 3.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
$\begin{array}{l} \ln x = 3 \\ x = e^{3} & Use the definition of the natural logarithm . \end{array}$
Figure 3 represents the graph of the equation. On the graph, the x-coordinate of the point at which the two graphs intersect is close to 20. In other words $e^{3} \approx 20.$ A calculator gives a better approximation: $e^{3} \approx 20.0855.$

Figure 3 The graphs of $y = \ln x$ and $y = 3$ cross at the point ${(e}^{3}, 3),$ which is approximately (20.0855, 3).

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Use a graphing calculator to estimate the approximate solution to the logarithmic equation $2^{x} = 1000$ to 2 decimal places.

How did it go?