find log 48 to the base 24 in terms of A if log 36 to the base 12 is A Share with your friends Share 16 Rishabh Mittal answered this Given:- log1236=ATo find:- log2448 First, we will simplify the log2448 , log2448 = log2424×2 = log2424 + log242 since logxy=logx+logy = 1 + log242 since logxx=1 = 1 + 1log224 since logax=1logxa = 1 + 1log28×3 = 1 + 1log28+log23 = 1 + 1log223+log23 = 1 + 13log22+log23 as logxn=nlogx = 1 + 13+log23 ...eqn1 as log22=1We have given that, log1236=A log1262=A 2log126=A log126=A2 1log612=A2 1log66×2=A2 1log66+log62=A2 11+log62=A211+1log26=A211+1log22×3=A211+1log22+log23=A211+11+log23=A211+log23+11+log23=A21+log232+log23=A22+2log23 =2A+Alog232log23-Alog23=2A-22-Alog23=2A-2log23=2A-22-APutting the value of log2 in eqn(1)1 + 13+log23=1 + 13+2A-22-A=1 + 132-A+2A-22-A=1 + 2-A6-3A+2A-2= 6-3A+2A-2+2-A6-3A+2A-2=6-2A4-A=23-A4-ASo, value of log2448 is 23-A4-A 53 View Full Answer
