Question

Simplify log10 625 - log10 25 + log10 4.​

Answer 1

Correct answer is 604

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Step-by-step explanation:- _________________________________

since , log 10 = 1

then this will become ..

625 - 25 + 4 ,

so ans will come 604

Thnk you ..

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Answer 2

SOLUTION

TO SIMPLIFY

$\displaystyle \sf{ log_{10}(625) - log_{10}(25) + log_{10}(4) }$

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

$\displaystyle \sf{ log_{10}(625) - log_{10}(25) + log_{10}(4) }$

$\displaystyle \sf{ = log_{10} \bigg( \frac{625}{25} \bigg) + log_{10}(4) }$

$\displaystyle \sf{ = log_{10} ( 25) + log_{10}(4) }$

$\displaystyle \sf{ = log_{10} ( 25 \times 4) }$

$\displaystyle \sf{ = log_{10} ( 100) }$

$\displaystyle \sf{ = log_{10} ( {10}^{2} ) }$

$\displaystyle \sf{ =2 log_{10} ( 10) }$

$\displaystyle \sf{ =2 \times 1}$

$\displaystyle \sf{ =2}$

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