SOLUTION: If possible, solve the equation 1.7(2.8)^(4x)=7(4.6)^x. Give exact answers, not decimals. If there is more than one solution, enter a comma separated list of answers, and enter NO

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: If possible, solve the equation 1.7(2.8)^(4x)=7(4.6)^x. Give exact answers, not decimals. If there is more than one solution, enter a comma separated list of answers, and enter NO      Log On


   

Question 1168676: If possible, solve the equation 1.7(2.8)^(4x)=7(4.6)^x. Give exact answers, not decimals. If there is more than one solution, enter a comma separated list of answers, and enter NONE if there are no solutions.
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1.7%282.8%29%5E%284x%29=7%284.6%29%5Ex........take log of both sides
log%281.7%282.8%29%5E%284x%29%29=log%287%284.6%29%5Ex%29
log%281.7%29%2Blog%28%282.8%29%5E%284x%29%29=log%287%29%2Blog%28%284.6%29%5Ex%29
log%28%282.8%29%5E%284x%29%29-log%28%284.6%29%5Ex%29=log%287%29-log%281.7%29
%284x%29log%28%282.8%29%29-+x%2Alog%28%284.6%29%29=log%287%29-log%281.7%29
x%284log%28%282.8%29%29-+log%28%284.6%29%29%29=log%287%29-log%281.7%29
x=%28log%287%29-log%281.7%29%29%2F%284log%28%282.8%29%29-+log%28%284.6%29%29%29->exact answer




Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
see the worksheet below.



step 1 is the equation.
step 2 divides both sides of the equation by 1.7
step 3 divides both sides of the equation by 4.6^x.
step 4 takes the log of both sides of the equation.
step 5 converts log(a/b) to log(a) - log(b).
step 6 converts log(a^x) to x*log(a).
step 7 factors out the x on the left side of the equation.
step 8 divides both sides of the equation by (4log(2.8)-log(4.6)).
step 9 solves for x.

the answer is an irrational number and so can't be converted to a fraction.

if you need to have everything in fraction form, then go back to step 8 and convert 1.7 and 2.8 and 4.6 to a fraction.
you will get: 


                              log(70/17)
              x =   -----------------------------
                       4*log(14/5) - log(23/5)