SOLUTION: express x in terms of log 10 : 4^x-2 = 7^3x+1 I don't understand how I am suppose to set up this problem or how to do it. :( any help (stepbystep etc.) would be really really ap

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: express x in terms of log 10 : 4^x-2 = 7^3x+1 I don't understand how I am suppose to set up this problem or how to do it. :( any help (stepbystep etc.) would be really really ap      Log On


   

Question 400077: express x in terms of log 10 : 4^x-2 = 7^3x+1
I don't understand how I am suppose to set up this problem or how to do it. :( any help (stepbystep etc.) would be really really appreciated thanks!
Found 2 solutions by ewatrrr, josmiceli:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Let log indicate a base of ten 

 4^x-2 = 7^3x+1

(x-2)log4 = (3x + 1)log7

  xlog4 - 2log4 = 3xlog7 + log7

    -2log4 -log7 = x(3log7 - log4)

    -%282log4+%2Blog7%29%2F%283log7+-+log4%29+=+x

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
4%5E%28x-2%29+=+7%5E%283x%2B1%29
4%5Ex+%2A+4%5E%28-2%29+=+7%5E%283x%29+%2A+7
Take the log base 10 of both sides
x%2Alog%284%29+-+2%2Alog%284%29++=+3x%2Alog%287%29+%2B+log%287%29
3x%2Alog%287%29+-+x%2Alog%284%29+=+-2%2Alog%284%29+-+log%287%29
x%2A%28log%284%29+-+3%2Alog%287%29%29+=+2%2Alog%284%29+%2B+log%287%29
x+=+%282%2Alog%284%29+%2B+log%287%29%29+%2F+%28log%284%29+-+3%2Alog%287%29%29