Question

Sabendo-se que log(x) base A = 2, logb(x) base B = 3 e logc(x) base C = 5, calcule:
a)logAB(x)
b)logABC(x)
c)log ab/c (x)

Answer 1

Ola Cicero

loga(x) = 2
logb(x) = 3
logc(x) = 5

log(x) = 2*log(a)
log(x) = 3*log(b)
log(x) = 5*log(c)

log(a) = log(x)/2
log(b) = log(x)/3
log(c) = log8x)/5

logab(x) = log(x)/(log(a) + log(b))
logab(x) = log(x)/(log(x)*(1/2 + 1/3) 

(1/2 + 1/3) = 5/6

logab(x) =  6/5 

logabc(x) = log(x)/log(x) *(1/2 + 1/3 + 1/5) 

(1/2 + 1/3 + 1/5) = 31/30

logabc(c) = 30/31

logab/c(x) = log8x)/log(x) * (1/2 + 1/3 - 1/5)

(1/2 + 1/3 - 1/5) = 19/30

logab/c(x) = 30/19 

.