Question

Given log 2 = 0.3010, log 3 = 0.4771, log 5 = 0.6990 and log 7 = 0.8451. using lagrange's formula, find log 47.

Answer 1

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Answer 2

Answer:

Concept :

The inverse function of exponentiation in mathematics is called the logarithm. In other words, the base b of a fixed number must be raised in order to create the specified number x, and the logarithm of that number is the exponent. The logarithm counts the number of times the same factor appears when multiplied repeatedly in the simplest case; for instance, since 1000 = 10 x 10 x 10 = 103, the logarithm base 10 of 1000 is 3, or log10 (1000) = 3. When there is little possibility of mistake or when the base is irrelevant, such as in big O notation, the logarithm of x to base b is written as logb (x), logb x, or even without the explicit base, log x.

Explanation:

log 47 =  log( $7^{2}$-2)

= log  $7^{2}$ / log 2

= 2log7 / log2

= 2*0.8451 / 0.3010

= 1.6902 / 0.3010

= 5.6152

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