SOLUTION: Solve a)7^-x=3 b)5^3x=41 c) 3^(1-x)=5 Can you please help me out? Thanks so much in advance:) Can you please show the work it will help me understand better:) thanks again

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve a)7^-x=3 b)5^3x=41 c) 3^(1-x)=5 Can you please help me out? Thanks so much in advance:) Can you please show the work it will help me understand better:) thanks again      Log On


   

Question 742296: Solve
a)7^-x=3
b)5^3x=41
c) 3^(1-x)=5
Can you please help me out? Thanks so much in advance:)
Can you please show the work it will help me understand better:) thanks again
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve
a)7%5E%28-x%29 = 3
therefore:
log%287%5E%28-x%29%29 = log(3)
use the log equiv of exponents
-x*log(7) = log(3)
-x = log%283%29%2Flog%287%29
using the log feature on your calc
-x = .564575
x has to be positive, mult both sides by -1
x = -.564575
Check this on a calc enter 7^(-(-.564575)) results: 2.9999 ~ 3
:
:
b)5%5E%283x%29 = 41
do this the same way
3x*log(5) = log(41)
3x = log%2841%29%2Flog%285%29
3x = 2.307372
x = 2.307372%2F3
x = .769124
Check on a calc; enter 5^(3*.769124)
:
:
c) 3%5E%28%281-x%29%29 = 5
(1-x)*log(3) = log(5)
you should get
1 - x = 1.465
-x = 1.465 - 1
-x = .465
which is
x = -.465
:
You can check this on on the calc, (remember minus a minus is plus)