SOLUTION: 16. 2log3(a) - log3(a+4)= 2 17. logz(x)= 3logz(p)+ 1/2logz(r)-logz(q) express in p,q, and r thank you please show work.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 16. 2log3(a) - log3(a+4)= 2 17. logz(x)= 3logz(p)+ 1/2logz(r)-logz(q) express in p,q, and r thank you please show work.      Log On


   



Question 126601This question is from textbook amscos preparing for the regents examination mathematics B
: 16. 2log3(a) - log3(a+4)= 2

17. logz(x)= 3logz(p)+ 1/2logz(r)-logz(q)
express in p,q, and r
thank you please show work.
This question is from textbook amscos preparing for the regents examination mathematics B

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2log3(a) - log3(a+4)= 2
Keep the base in mind:
loga^2 - log(a+4) = 2
log[a^2/(a+4)] = 2
----------
Apply the base:
a^2/(a+4) = 3^2
a^2 = 9a+36
a^2-9a-36 = 0
(a-12)(a+3)=0
a = 12 or a = -3
=------------------
17. logz(x)= 3logz(p)+ 1/2logz(r)-logz(q)
express in p,q, and r
Keep the base in mind:
logx = logp^3 + logr^(1/2) - logq
logx = log[p^3*r^(1/2)/q]
Since the logs are equal the anti-logs are equal
----------------
x = [p^3*r^(1/2) / q]
============================
Cheers,
stanH.