Exercise 32 Page 496

To solve the given exponential inequality, we will use the Inequality Property of Logarithmic Functions.

Using this property, we can rewrite the exponential inequality as a logarithmic inequality. 5^(p-2) ≥ 2^p ⇔ log 5^(p-2) ≥ log 2^pTo solve the above logarithmic inequality, we need to recall the Power Property of Logarithms.

Let's use it and solve the inequality!

The final step to isolate p will be to divide both sides of the inequality by log 5 - log 2. Before we take this step, let's stop for a moment and think about the sign of the expression. 5>2 ⇔ log 5 > log 2 Because log 5 is greater than log 2, we know that the difference between log 5 and log 2 will be a positive number. Therefore, to divide by this value, we do not have to reverse the inequality sign.

Finally, we can write our answer in set-builder notation. { p | p ≥ 3.5129 }