Logaritmo #2

Algebra Level 1

If (log 2 = 0,3), (log 100 = 2), (log x = 1,3) and...

( x + log 1000 + log x + log 5 = y),

what is the value of y?

20 50 35 25

Victor Porto by Victor Porto , 22, Brazil

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1 solution

F i r s t w e n e e d t o f i n d t h e v a l u e o f x N o w l o g x = 1.3 l o g x = 1 + 0.3 l o g x = l o g 10 + l o g 2 l o g x = l o g 20 S o , x = 20 N o w , l e t ′ s c a l u c l a t e l o g 5 : l o g 5 = l o g 1000 20 l o g 5 = l o g 1000 − l o g 20 l o g 5 = 3 − 1.3 l o g 5 = 1.3 P u t t i n g v a l u e s i n t h e g i v e n e q u a t i o n : x + l o g 1000 + l o g x + l o g 5 = y 20 + 3 + 1.3 + 0.7 = y y = 25 First\quad we\quad need\quad to\quad find\quad the\quad value\quad of\quad x\\ Now\quad log\quad x\quad =\quad 1.3\\ \quad \quad \quad \quad log\quad x\quad =\quad 1\quad +\quad 0.3\\ \quad \quad \quad \quad log\quad x\quad =\quad log10\quad +\quad log2\\ \quad \quad \quad \quad log\quad x\quad =\quad log20\\ So,\quad x\quad =\quad 20\\ \\ Now,\quad let's\quad caluclate\quad log{ 5 }:\\ log{ 5 }\quad =\quad log{ \frac { 1000 }{ 20 } }\quad \\ log{ 5 }\quad =\quad log{ 1000 }-log{ 20 }\\ log{ 5 }\quad =\quad 3-1.3\\ log5\quad =\quad 1.3\\ \\ Putting\quad values\quad in\quad the\quad given\quad equation:\\ x\quad +\quad log1000\quad +\quad logx\quad +\quad log5\quad =\quad y\\ 20\quad +\quad 3\quad +\quad 1.3\quad +\quad 0.7\quad =\quad y\\ y\quad =\quad 25

Cheers!!:):)

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Dear plz rectifyme if i am wrong the solution should be log5=log(100/20)=log100-log20=2-1.3=0.7 Regards

Niaz Ghumro - 6 years, 7 months ago

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