SOLUTION: Solve the exponential equation algebraically. Approximate the result to three decimal places. (Enter your answers as a comma-separated list.) 4^(1 − x) = 315

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the exponential equation algebraically. Approximate the result to three decimal places. (Enter your answers as a comma-separated list.) 4^(1 − x) = 315       Log On


   

Question 962607: Solve the exponential equation algebraically. Approximate the result to three decimal places. (Enter your answers as a comma-separated list.)
4^(1 − x) = 315
Found 3 solutions by ankor@dixie-net.com, MathLover1, MathTherapy:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the exponential equation algebraically. Approximate the result to three decimal places. (Enter your answers as a comma-separated list.)
4^(1 − x) = 315
use natural logs
ln%284%5E%28%281-x%29%29%29+=+ln%28315%29
the log equiv of exponents
(1-x)ln(4) = ln(315}
(1-x) = ln%28315%29%2Fln%284%29
use you calc
1 - x = 4.1496
-x = 4.1496 - 1
-x = 3.1496
mult both sides by -1
x = -3.1496
:
:
Check this on your calc, enter: 4^(1-(-3.1496))

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

4%5E%281-x%29+=+315.......use log to solve
log%284%5E%281-x%29%29+=+log%28315%29
%281-x%29log%284%29+=+log%289%2A35%29
%281-x%29+=+log%283%5E2%2A35%29%2Flog%284%29
1-x+=+%28log%283%5E2%29%2Blog%287%2A5%29%29%2Flog%284%29
1-x+=+%282log%283%29%2Blog%287%29%2Blog%285%29%29%2Flog%282%5E2%29
1-%282log%283%29%2Blog%287%29%2Blog%285%29%29%2F2log%282%29=x
x=%282log%282%29-2log%283%29-log%285%29-log%287%29%29%2F2log%282%29...exact solution

x=%280.60205999132796-0.9542425094-0.69897-0.84509804%29%2F%280.60205999132796%29
x=%28-1.89625055807204%29%2F%280.60205999132796%29
x=-3.149604
x=-3.149 or x=-3.150

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Solve the exponential equation algebraically. Approximate the result to three decimal places. (Enter your answers as a comma-separated list.)
4^(1 − x) = 315
4%5E%281+-+x%29+=+315 ------- Exponential form

log+%284%2C+315%29+=+1+-+x ----- Logarithmic form

x+=+1+-+log+%284%2C+315%29, or -+3.1496, or highlight_green%28-+3.150%29