XXSumanXxidn
Answered

Get comprehensive answers to your questions with the help of IDNLearn.com's community. Our experts provide timely, comprehensive responses to ensure you have the information you need.

If [tex]\sf a = log_92[/tex] and [tex]\sf b = log_54[/tex], find [tex]\sf log_615[/tex] in terms of a and b.​

Sagot :

Mhanifaidn

Answer:

  • (4a + b)/(2ab + b)

Step-by-step explanation:

Given

  • a = log9 2
  • b = log5 4

To find

  • log6 15 in terms of a and b

Solution

Rewrite the given

  • log9 2 = a ⇒ log2/log9 = a ⇒ 1/2*log2/log3 = a ⇒  log3 = 1/2*log2/a
  • log5 4 = b ⇒ log4/log5 = b ⇒ log5 = 2*log2/b

Rewriting the log6 15:

  • log6 15 = log15/log6= (log 5 + log3)/(log2 + log3)

Substitute as follows:

  • (log 5 + log3)/(log2 + log3) =
  • (2*log2/b + 1/2*log2/a)/(log2 + 1/2*log2/a) =
  • (2/b + 1/(2a))/(1 + 1/(2a)) =
  • (4a + b)/2ab ÷ (2a + 1)/2a =
  • (4a + b)/(2ab + b)
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.