Question

find the value of log 10 to the base 1000​

Answer 1

SOLUTION

TO EVALUATE

$\displaystyle \sf{ log_{1000}(10) }$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on logarithm that

$\sf{1. \: \: \: log( {a}^{n} ) = n log(a) }$

$\sf{2. \: \: log(ab) = log(a) + log(b) }$

$\displaystyle \sf{3. \: \: log \bigg( \frac{a}{b} \bigg) = log(a) - log(b) }$

$\sf{4. \: \: log_{a}(a) = 1}$

EVALUATION

$\displaystyle \sf{ log_{1000}(10) }$

$\displaystyle \sf{ = \frac{1}{log_{10}(1000)} }$

$\displaystyle \sf{ = \frac{1}{log_{10}( {10}^{3} )} }$

$\displaystyle \sf{ = \frac{1}{3 \: log_{10}( {10}^{} )} }$

$\displaystyle \sf{ = \frac{1}{3 \times 1} }$

$\displaystyle \sf{ = \frac{1}{3} }$

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Answer 2

Answer:

but the answer will be 1/3