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General Chemistry Principles, Patterns, and Applications, 2011

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20.50.026<br />

Solution:<br />

a. ln(22 × 18.6) = ln(22) + ln(18.6) = 3.09 + 2.923 = 6.01. Alternatively, 22 × 18.6 = 410;<br />

ln(410) = 6.02.<br />

ln(0.512.67) = ln(0.51) - ln(2.67)<br />

b. = -0.67 - 0.982 = -1.65. (0.19) = −1.66.<br />

Alternatively, 0.512.67 = 0.19;ln<br />

c. ln(0.079 × 1.485) = ln(0.079) + ln(1.485) = −2.54 + 0.395 = −2.15. Alternatively,<br />

0.079 × 1.485 = 0.12; ln(0.12) = −2.12.<br />

ln(20.50.026) = ln(20.5) - ln(0.026)<br />

d. = 3.0204 - (-3.65) = 6.67. (790) = 6.67.<br />

Alternatively, 20.50.026 = 790;ln<br />

The answers obtained using the two methods may differ slightly due to rounding errors.<br />

S K I L L BUILDER ES4<br />

Calculate the natural logarithm of each number.<br />

a. 34 × 16.5<br />

b. a. 2.100.052 0.402 × 3.930<br />

a. 0.16410.7<br />

Solution:<br />

a. 6.33<br />

b. 3.70<br />

c. 0.457<br />

d. −4.178<br />

[1] On some calculators, pressing [INV] <strong>and</strong> then [ln x] is equivalent to pressing [ex].<br />

11.10 End-of-Chapter Material<br />

A P P L I C A T I ON PR OBLEMS<br />

Please be sure you are familiar with the topics discussed in Essential Skills 6 (Section 11.9 "Essential Skills<br />

6") before proceeding to the Application Problems. Problems marked with a ♦ involve multiple concepts.<br />

Saylor URL: http://www.saylor.org/books<br />

Saylor.org<br />

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