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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 :

mhanifa

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)
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