Question

log 45 na base 3 como resolver?
log (x-1) na base 1/3 = -2 ?
log(2x+1) - log(5x-3)=-1 na base 3?

Answer 1

45 = 3² . 5
log[3] (3² . 5)
log[3] 3² + log[3]5
2log[3]3 + log[3]5
2.1+log[3]5
2 + log[3] 5
============
(1/3)^-2 = x-1
3² = x-1
9+1=x
x = 10
=============
log[3]  (2x+1) = -1
           (5x-3)
3^-1 = 2x+1
           5x-3
1 = 2x+1
3    5x-3
6x+3=5x-3
x = -3-3
x= -6