SOLUTION: if 3^x =54, then which of the following must be true? The answer is 3<x<4. How do you answer this?

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: if 3^x =54, then which of the following must be true? The answer is 3<x<4. How do you answer this?      Log On


   

Question 702317: if 3^x =54, then which of the following must be true? The answer is 3
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

3%5Ex+=54......use log to solve for x

log%28%283%5Ex%29%29+=log%28%2854%29%29

xlog%28%283%29%29+=log%28%2854%29%29

x+=log%28%2854%29%29%2Flog%28%283%29%29

x+=log%28%2854%29%29%2Flog%28%283%29%29

x+=log%28%2827%2A2%29%29%2Flog%28%283%29%29
x+=log%28%283%5E3%2A2%29%29%2Flog%28%283%29%29

x+=%28log%28%283%5E3%29%29%2Blog%28%282%29%29%29%2Flog%28%283%29%29

x+=%283log%28%283%29%29%2Blog%28%282%29%29%29%2Flog%28%283%29%29

x+=3log%28%283%29%29%2Flog%28%283%29%29%2Blog%28%282%29%29%2Flog%28%283%29%29



x+=3%2Blog%28%282%29%29%2Flog%28%283%29%29

x+=3%2B0.630929753571457

x+=3.630929753571457.......so, the answer is 3%3Cx%3C4
3%3C3.630929753571457%3C4....true