Solving and Evaluating with Calculators

Besides taking too long, the round-off error will very likely be too large for your answer to be counted "correct". Instead, get in the habit of doing as many steps as you can all at once within the calculator's memory.

If you use a graphing calculator, typeset the entire expression at once, being careful with your parentheses. If you typeset without parentheses, as shown below:

...then you will get the wrong value, because the calculator thought you meant "divide the natural log of 350 by 3, and then divide this by the log of 2, and then subtract 4"

What you need to enter is this:

...which is "the natural log of the quotient of 350 and 3, divided by the natural log of 2, and then subtracting 4 from this". Parentheses can make a big difference on graphing calculators!

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• Solve 2e^x + 5 = 115, and round to three decimal places.

Grab your calculator and make sure you can arrive at the above decimal approximation. Check your calculator for the rest of the examples, too. You don't want to wait until the next test to learn how to do the inputs correctly.

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• Solve 1000^0.12x = 25,000, and round to three decimal places.

Note that the expression could have been simplified differently, by using log properties and rules, before entering it into the calculator:

This is equivalent to the previous form of the answer. I am pointing this out because you may need to be flexible with the form of your final answer.

For instance, if you had come up with the first form of the answer, but the back of the book gave the second form of the answer, then you would need to be able to recognize that the two forms are actually the same thing. The same goes for multiple-choice tests, where your form of the answer might be different in form from, but equivalent in value to, one of the given choices.

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• Solve 250(1.04)^x = 1000, and round to three decimal places.

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The equation in the above exercise is of the form used for compound-interest problems. If this question had been stated in terms of interest rates and investments, the above answer would have stood for "35.346 years", or about thirty-five years and four months.

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As long as you do your steps clearly and completely, and keep your log rules in mind, along with the definitions of exponentials and logs, you shouldn't have too much trouble in solving these equations. Just remember to keep your work as "exact" as you can for as long as you can; wait to approximate things in your calculator until the very end, if at all possible.