problem with god damn logs (1 Viewer)

[ryanox]

if log (base b) a= 3.75 and log (base b) c= 1.25 find the value of:
(a) log (base a) ab
(b) log (base b) (a/c)
(c) log (base b) (ac)2
(d) log (base c) a

 

[Riviet]

(a) log_a(ab)=log_aa + log_ab
= 1 + log_ab
= 1 + log_bb/log_ba
= 1 + 1/3.75
= 19/15

(b) log_b(a/c)=log_ba - log_bc
=3.75 - 1.25
=2.5

(c) Did you mean log_b(ac)² ?
If so, then
log_b(ac)²=2log_bac
=2(log_ba + log_bc)
=2(3.75 + 1.25)
=2 x 5
=10

(d) log_ca=log_ba/log_bc
=3.75/1.25
=3