Question

If y = log 750 then y is equal to
(A) 2 log 5 + log 3+1
(C) 2 log 5 + 2 log 2+1
(B) 3+ log 3 - 2 log 2
(D) 2+ log 3 - 2 log 2
please as fast as you can​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

If y = log 750 then y is equal to

(A) 2 log 5 + log 3+1

(C) 2 log 5 + 2 log 2+1

(B) 3+ log 3 - 2 log 2

(D) 2+ log 3 - 2 log 2

FORMULA TO BE IMPLEMENTED

We are aware of the formula on logarithm that

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

$\sf{2. \: log_{a}( {b}^{n} ) = n log_{a}(b) \: }$

EVALUATION

Here the base of the logarithm is 10

$\sf{y = log_{10}(750) }$

$\sf{= log_{10}(3 \times 10 \times 25) }$

$\sf{= log_{10}(3) + log_{10}(10) + log_{10}(25) }$

$\sf{= log_{10}(3) + 1 + log_{10}( {5}^{2} ) } \: \: ( \: by \: formula \: 1 \: )$

$\sf{= log_{10}(3) + 1 + 2log_{10}( 5 ) \: \: \: ( \: by \: formula \: 2 )}$

$\sf{ = 2 log(5) + log(3) + 1 }$

FINAL ANSWER

The correct option is

$\sf{(A) \: \: 2 log(5) + log(3) + 1}$

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Answer 2

Option A

Step-by-step explanation:

Option A id the correct answer