Question

Find the value of logarithm of 0.0001 to the base 0.001

Answer 1

Hope it helps ................

Answer 2

Concept

Log x to the base a can be written as log x to the base b upon log a to the base b.

Given

logarithm of 0.0001 to the base 0.001

Find

we need to find the value of the given expression

Solution

We have

logarithm of 0.0001 to the base 0.001

This can be written as

$\frac{log 0.0001}{log 0.001}$ (both to the base 10)

= $\frac{log 10^{-4} }{log 10^{-3} }$

= $\frac{-4 log 10}{-3 log 10}$

Log a to the base a is equal to 1, similarly here log 10 to the base 10 will be equal to 1

= $\frac{-4 *1}{- 3 * 1}$

= 4/3

Hence, the value of logarithm of 0.0001 to the base 0.001 is 4/3.

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