Page 313 - Theory and Problems of BEGINNING CHEMISTRY

302 SCIENTIFIC CALCULATIONS [APP.

On the calculator, the reciprocal 1/x key takes the reciprocal of whatever value is in the display. To get
the reciprocal of a/b, enter the value of a, press the division ÷ key, enter the value of b, press the equals =
key, and finally press the reciprocal 1/x key. Alternatively, enter the value of b, press the division key, enter the
value of a, and press the equals key. The reciprocal of a/b is b/a.
The reciprocal key is especially useful if you have a calculated value in the display that you want to use as
a denominator. For example, if you want to calculate a/(b + c) and you already have the value of b + c in the
display, you divide by a, press the equals key, and then press the reciprocal key to get the answer. Alternatively,
with the value of b + c in the display, you can press the reciprocal key and then multiply that value by a.

a 1
= a
b + c b + c

EXAMPLE A.22. The value equal to 1.77 + 1.52 = 3.29 is in the display of your calculator. What keystrokes should you
use to calculate the value of the following expression?
3.08
1.77 + 1.52

Ans. 1/x × 3 . 0 8 = or ÷ 3 . 0 8 = 1/x
The display should read 0.93617 ···.

Logarithms and Antilogarithms
Determining the logarithm of a number or what number a certain value is the logarithm of (the antilogarithm
of the number) is sometimes necessary. The logarithm log key takes the common logarithm of the value in the
display. The 10 x key, or the INV key or the 2ndF key followed by the log key, takes the antilogarithm of
the value in the display. That is, this sequence gives the number whose logarithm was in the display.
The ln key takes the natural logarithm of the value in the display. The e x keyorthe INV key or the
2ndF key followed by the ln key, yields the natural antilogarithm of the value in the display.

EXAMPLE A.23. What sequence of keystrokes is required to determine (a) the logarithm of 1.15 and (b) the antilogarithm
of 1.15? Reminder: Some calculators require log to be entered before the number. Check the owner’s manual.
Ans. (a) 1 . 1 5 log

(b) 1 . 1 5 10 x or 1 . 1 5 2ndF log or 1 . 1 5 INV log

EXAMPLE A.24. What sequence of keystrokes is required to determine (a) the natural logarithm of 5.1/5.43 and (b) the
natural antilogarithm of 5.1/5.43?
Ans. (a) 5 . 1 ÷ 5 . 4 3 = ln
(b) 5 . 1 ÷ 5 . 4 3 = 2ndF ln
In part a, be sure to press = before ln so that you take the natural logarithm of the quotient, not that of the
denominator. In part b, press = before 2ndF (or INV ).

EXAMPLE A.25. Write the sequence of keystrokes required to solve for x, and calculate the value of x in each case:

(a) x = log(2.22/1.03) (b) x = 2.22/log1.03