I am trying to solve for x in the equation:
2(5)^x = 3^(x+1)
I know the answer should be x=0.79375 because I've graphed them as functions and found the intersect, as well as run the equation through wolfram.
However, I try to find this by solving for myself and I always seem to come up with x=0.51815.
I have:
2(5)^x = 3^(x+1)
xLog(25) = (x+1)Log3
xLog25 = xLog3 + Log3
xLog25 - xLog3 = Log3
x(Log25 - Log3) = Log3
x(Log25 - Log3)/(Log25 - Log3) = Log3/(Log25 - Log3)
x = Log3/(Log25 - Log3) which is 0.51815
I must be making a mistake somewhere but I just don't see it. Any help is appreciated, thanks!
No, the equation given to me was simply 2 x 5^x = 3^(X+1), I put both side into logarithmic form to try and solve it (context is that this is what I'm suppose to do for every question in this assignment).
I skipped out a step when describing what I did, my first step was to log both sides, so the equation became 2log5^x = log3^(x+1). Then I used the power law to take the exponent of the logs and change it to the coefficient. So the equation became 2xlog5 = (X+1)log3. And I also did the reverse on the left side, took the coefficient 2 and brought it back into the log, giving me xlog5^2, which is xlog25. Am I making a mistake somewhere in that process?
Oh I see, my mistake was not applying the log to the entire left side of the equation (I only applied the log to the 5^x, and left the 2 alone during this step). Basic algebra error, I had a feeling I was messing up something basic like that. Thanks very much!
EDIT: Thanks deepashree as well!