SOLUTION: please help me with this equation.thanks so much If log 2=.3010 log3=.4771, find the numerical value of x in 3^x+2=405.

Algebra ->  Rational-functions -> SOLUTION: please help me with this equation.thanks so much If log 2=.3010 log3=.4771, find the numerical value of x in 3^x+2=405.      Log On


   

Question 74031: please help me with this equation.thanks so much
If log 2=.3010 log3=.4771, find the numerical value of x in 3^x+2=405.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%5Ex%2B2=405
3%5Ex=403Subtract 2 from both sides
log_%5B3%5D%283%5Ex%29=log_%5B3%5D%28403%29Take the log base 3 of both sides
x=log_%5B3%5D%28403%29
Use the change of base formula
log_%5Bb%5D%28a%29=%28log+%28a%29%29%2F%28log%28b%29%29
x=%28log+%28403%29%29%2F%28log%283%29%29Remember the default base is 10
x=2.605305%2F.4771Use given value log3=.4771 and evaluate log 403
x=5.46071Approximately
Hope this helps.


Check:
3%5Ex%2B2=405Plug in x=5.46071
3%5E%285.46071%29%2B2=405
403.107%2B2=405
405.107=405Which is close but off due to roundoff errors.