If and , find in terms of a and b.

(4a + b)/(2ab + b)

Step-by-step explanation:

Givena = log9 2b = log5 4To findlog6 15 in terms of a and bSolution

Rewrite the given

log9 2 = a ⇒ log2/log9 = a ⇒ 1/2*log2/log3 = a ⇒  log3 = 1/2*log2/alog5 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)