please do urgent ..please guys Mark on brainlist on you
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22.
Given that
log (3+√5) + log (3-√5)
We know that
log ab = log a + log b
=> log [(3+√5)(3-√5)]
This is in the form of (a+b)(a-b)
Where a = 3 and b = √5
We know that
(a+b)(a-b) = a²-b²
=> log [(3)²-(√5)²]
=> log(9-5)
=> log 4
Answer :-
log (3+√5) + log (3-√5) = log 4
23)
Given that
log √x (x) + log c² (c)
=> log x^1/2 (x) + log c² (c)
We know that
log a^m (b^n) = m/n log a (b)
=> 1/2 log x (x) + 2 log c (c)
We know that
log a ( a) = 1
=> (1/2)(1) + 2(1)
=> (1/2)+2
=> (1+4)/2
=> 5/2
Answer:-
log √x (x) + log c² (c) = 5/2
[(x) ,(c) , (a) represents the bases ]
Used formulae:-
- (a+b)(a-b) = a²-b²
- log a^m (b^n) = m/n log a (b)
- log a ( a) = 1
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