Question

if 3^a =4^b=12^c then show that c=ab/a+b​

Answer 1

Please refer the image file attached for solution.

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Answer 2

Answer:

• 3^a =4^b=12^c= k
• 3^a= k ⇒ 3= k^1/a
• 4^b=k ⇒ 4= k^1/b

12^c=k

12^c=3^c*4^c= k^c/a*k^c/b= k^(c/a+c/b)

k= k^(c/a+c/b)

• c/a+c/b=1
• c(a+b)=ab
• c= ab/(a+b)