If A= log(base2)2 and
B= log(base2)3 write the following in terms of A and B.
a) log(base2) (20.25)

Question

If A= log(base2)2 and 
B= log(base2)3 write the following in terms of A and B. 
a) log(base2) (20.25)

anonymous · Answer

log20.25=log4.5.5.5
log2^2+log5^3
2log2+3log5
2log2=2A

3log(5+1-1)=3(log6-log1) adding 1 and subtracting 1 wont change the solution.
3(log2.3-log1)
3(log2+log3-log1)
log1=0
3(log2+log3)=3A+3B

2A+3A+3B=5A+3B

ididnt type the bases
all bases are 2

remember the log rules
loga.b=loga+logb
log(a/b)=loga-logb
loga^n=nloga

all must have same bases

anonymous · Answer

log(20.25) = (log 20 + log 25) = (log (2.5.2) + log (25))= [2log(2)+ 3log(5)]
2A+ 3log(5 +1-1)=2A+3log(6/1)=2A + 3(log3 + log 2- log1)=2A+3A+3B= 5A +3B