SOLUTION: Given log(base 3)10= 2.0959 find an approximation for each logarithm a) log(base 3)1000 b) log(base 3)30 c) log(base 3)√03 d) log(base 3) (100/9) Can you please help m

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Given log(base 3)10= 2.0959 find an approximation for each logarithm a) log(base 3)1000 b) log(base 3)30 c) log(base 3)√03 d) log(base 3) (100/9) Can you please help m      Log On


   

Question 744921: Given log(base 3)10= 2.0959 find an approximation for each logarithm
a) log(base 3)1000
b) log(base 3)30
c) log(base 3)√03
d) log(base 3) (100/9)
Can you please help me out? Thanks so much in advance:)
Can you also show all the steps because it would help me understand :)
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
rewrite in terms given...
Given log(base 3)10= 2.0959 find an approximation for each logarithm
a)
log(base 3)1000
log(base 3)(10^3)
3*log(base 3)(10)
3*2.0959
6.2877
.
b)
log(base 3)30
log(base 3)(3*10)
log(base 3)3 + log(base 3)(10)
1 + 2.0959
3.0959
.
c)
log(base 3)√03
log(base 3)3^(1/3)
(1/3)log(base 3)3
(1/3)*1
1/3
.
d)
log(base 3) (100/9)
log(base 3)(100) - log(base 3)(9)
log(base 3)(10^2) - log(base 3)(3^2)
2log(base 3)(10) - 2log(base 3)(3)
2(2.0959) - 2(1)
4.1918 - 2
2.1918