Page:Elementary algebra (1896).djvu/384

366 ALGEBRA. Ex. Find by use of logarithms the value of 4.26 7.42 \times .058.

log {4.26 7.42 \times .058} = log 4.26 + log — + log -^ ° 7.42 X .058 ='7.42 .058 = log 4.26 + colog7.42 + colog .058 = .6294 +(9.1296 - 10)+ 1.2366 = 10.9956 - 10.

The number corresponding to this logarithm is 9.9.

In finding colog .058 we proceed as follows:

colog .058 = log 1 .058 = 10 - [log. 058] - 10 (Art. 447), .0o8 = 10 - [8.7634 - 10] - 10 (Art. 437), = 10 - 8.7634 + 10 - 10 = 1.2366.

449. Exponential Equations. Equations in which the unknown quantity occurs as an exponent are called exponential equations, and are readily solved by the aid of logarithms.

Ex. Find the value of x in 15^x = 28. Taking the logarithms of both sides of the equation, we have

log 15^x = log 28; x log 15 = log 28. x = {log 28 log 15} = {1.4472 1.1761} = 1.2305 +.

EXAMPLES XXXVIII. c.

Find by use of logarithms:

1. 24.051 .02456 .006705  .0203 2. {145.206 X (-7.564)}{ 448.1 x(-.2406)(-47.85)} 3. (742 8024)^3. 4. (-.0012045)^{3 5}. 5. {3 4.8 X 4 .002 X 5 442.6} {(18)^2 X .7^3 X (3.4562)^{1 2}} 6. {9.8149 X 80.8008} {8283 X (.0006412)^4}. 7. 845692.1 x .845856. 8. .00010101 x (7117.1)^6. 9. (285.42)1.4 x (5.672)3 20 3 .02 -124:89 10. 3 12.876 x .068 x (.005157)^2 29.029 X (52.81)^4 (.4)^9 11. 3^{x+2} = 405. 12. 10^{5-3x} = 2^{7-2x}. 13. 12^{3x-4} x 18^{7-2x} = 1458. 14. 2^x x 6^{x-2} = 5^{2x} x 7^{1-x}. 16. 3^{1-x-y} = 4^{-y}, 2^{2x-1} = 3^{3y-x}.

ordinary rules of multiplication and division.
 * Treat negative quantities occurring in logarithmic work as positive. When the numerical result is obtained, determine its sign by the