Many exponential and logarithmic equations cannot be solved algebraically as we did in this section. However, they can be solved graphically as was shown in the check of Example 8. In Exercises, solve the given equations graphically by use of a calculator.

2^x + 3^x = 50

Data from Example 8

Solve the logarithmic equation 2 log x − 1 = log(1 − 2x).

The calculator graph of y = 2 log x − 1 − log(1 − 2x) is shown in Fig. 13.19. The zero displayed on the screen shows that our answer is correct.

log.x log(1 - 2x) = 1 x 1 - 2x X = log: x 1 - 2x - = 1 = 10 x 10 20x x + 20x 10 = 0 -20 400 + 40 2 -10110