SOLUTION: Solve the following exponential equation. Make use of logarithms. Round answer to 3 decimal places. 200(1.22)t=13,960

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve the following exponential equation. Make use of logarithms. Round answer to 3 decimal places. 200(1.22)t=13,960       Log On


   

Question 1183126: Solve the following exponential equation. Make use of logarithms.
Round answer to 3 decimal places.
200(1.22)t=13,960
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

200%281.22%29%5Et=13960

%281.22%29%5Et=13960%2F200

%281.22%29%5Et=349%2F5............take log of both sides

log%28%281.22%29%5Et%29=log%28%28349%2F5%29%29

t%2Alog%28%281.22%29%29=log%28%28349%2F5%29%29

t=%28log%28%28349%29%29-log%28%285%29%29%29%2Flog%28%281.22%29%29

t=4.2456340097683265%2F0.19885085874516517

t=21.351


Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.


            Do it as simple as it  SHOULD  be done. 


Your starting equation is

    200%281.22%29%5Et = 13960  



Next, divide both sides by 200

    %281.22%29%5Et = 13960%2F200  



Next, simplify

    %281.22%29%5Et = 69.8   


Next, take logarithm base 10 of both sides 


    log%28%281.22%29%5Et%29 = log%28%2869.8%29%29


    t%2Alog%28%281.22%29%29 = 1.84386


    t = 1.84386%2Flog%28%281.22%29%29


    t=21.351     (approximately;  rounded)      ANSWER

Solved.


It is a standard mantra and a standard algorithm on solving exponential equations of this type.