SOLUTION: Will someone solve and explain this question: Q: Find x, correct to 3 significant figures, in the following: 3^x . 10^2x = 4 . 20^x-2

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Will someone solve and explain this question: Q: Find x, correct to 3 significant figures, in the following: 3^x . 10^2x = 4 . 20^x-2      Log On


   

Question 942774: Will someone solve and explain this question:
Q: Find x, correct to 3 significant figures, in the following:
3^x . 10^2x = 4 . 20^x-2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3%5Ex%2A10%5E%282x+%29=+4%2A+20%5E%28x-2%29....use logarithm

log%283%5Ex%2A10%5E%282x+%29%29=+log%284%2A+20%5E%28x-2%29%29

log%283%5Ex%29%2Blog%2810%5E%282x+%29%29=+log%284%29%2Blog%28+20%5E%28x-2%29%29

log%283%5Ex%29%2Blog%2810%5E%282x+%29%29=+log%284%29%2Blog%28+20%5Ex%2F20%5E2%29%29

log%283%5Ex%29%2Blog%2810%5E%282x+%29%29=+log%284%29%2Blog%28+20%5Ex%29-log%2820%5E2%29%29










x%2Alog%283%29%2Bx%2Alog%285%29=+-2log%282%29-2log%285%29

x%28log%283%29%2Blog%285%29%29=-2%28log%285%29+%2Blog%282%29%29

x=-2%28log%285%29+%2Blog%282%29%29+%2F%28log%283%29%2Blog%285%29%29

x=-2%280.69897%2B0.301%29%2F%280.477%2B0.69897%29

x=-2%280.99997%29%2F%281.17597%29

x=-1.99994%2F1.17597

x=-1.700672636206706

x=-1.701

if you check it, you get
0.0000612277=0.0000612277