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41. Corollary. The logarithm of the fourth term of a proportion is found by adding together the arithmetical complement of the logarithms of the first term and the logarithms of the second and third terms.

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2. Find the fourth term of the proportion

0.0138 0.319 = 76·5: x.

Ans. x 1768.3.

43. Problem. To solve the exponential equation

am,

by means of logarithms.

Solution. The logarithms of the two members of this equation give

hence

x log. a = log. m;

or

x =

log. m
log, a'

- log. log. a;

log. x = log. log. m

that is, the root of this equation is equal to the logarithm of m divided by the logarithm of a, and this quotient may be obtained by the aid of logarithms.

Exponential Equations.

44. EXAMPLES.

1. Solve the equation

6253125.

Solution. We have, from the tables,

and also

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log. 625 = 2.79588;

log. log. 3125 = log. 3·49485 = 0·54343
log. log. 625= log. 2·79588 = 0·44652
log. x = log. 1.25

x = 1.25.

0.09691;

hence

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