Question

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Explain what common logarithms are and how they are used to find the value of a logarithm that is not common.

Answer 1

A common logarithm is a logarithm to the base 10.
LOG(x) = a means that 10^a = x, so LOG(10)=1, LOG(100)=2, etc.

To find a logarithm of a different base, b, consider

Given x, we want y such that b^y = x.

Since b = 10^(LOG(b))
b^y = (10^LOG(b)) ^ y = x

We know that (10^m)^n = 10 ^ (m*n) so

x = 10 ^ (LOG(b)*y) and
LOG(x) = LOG(b)*y

so y = LOG(x) / LOG(b)

Answer 2

THANKS

Answer 3

u welcome