Question

log 3600 iis equal to ​

Answer 1

Answer:

Log 3600 is equal to a 2log6 1 b 6log2 1 c 2log6 2 d 6log2 2.

Answer 2

SOLUTION

COMPLETE QUESTION

log 3600 is equal to:

a) 2 log 6 + 2

b) 6 log 2 + 1

c) 6 log 2 + 2

d) 2 log 6 + 1

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

$\sf{ log(3600) }$

$\sf{ = log_{10}(3600) }$

$\sf{ = log_{10}(36 \times 100) }$

$\sf{ = log_{10}(36 ) +log_{10}(100) }$

$\sf{ = log_{10}( {6}^{2} ) + log_{10}( {10}^{2} ) }$

$\sf{ = 2 log_{10}( {6}^{} ) +2 log_{10}( {10}^{} ) }$

$\sf{ = 2 log_{10}( {6}^{} ) +(2 \times 1) }$

$\sf{ = 2 log_{10}( {6}^{} ) + 2}$

$\sf{ = 2 log_{}( {6}^{} ) + 2}$

FINAL ANSWER

Hence the correct option is a) 2 log 6 + 2

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