If log_2 3=a and log_5 2=b then log_(24) 50 is equal to? I guess this has to be done by using simple logarithmic rules, but I do not how to start. Answer in my booklet is (b+2)/(b(a+3))

clovnerie0q

clovnerie0q

Answered question

2022-09-06

If log 2 3 = a and log 5 2 = b then log 24 50 is equal to?
I guess this has to be done by using simple logarithmic rules, but I do not how to start. Answer in my booklet is b + 2 b ( a + 3 )

Answer & Explanation

Yuliana Griffith

Yuliana Griffith

Beginner2022-09-07Added 6 answers

hint: log 24 50 = log 24 ( 2 5 2 ) = log 24 2 + 2 log 24 5 = 1 log 2 24 + 2 log 5 24 = 1 3 + log 2 3 + 2 3 log 5 2 + log 5 2 log 2 3 = 1 a + 3 + 2 3 b + a b = . . .
Kelton Bailey

Kelton Bailey

Beginner2022-09-08Added 1 answers

Clearly, 3 = 2 a , 5 = 2 1 / b , which shows
24 = 2 3 3 = 2 a + 3 ,   50 = 2 5 2 = 2 1 + 2 / b = 2 ( b + 2 ) / b
So 50 = 24 ( b + 2 ) / ( b ( a + 3 ) )
QED

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