SOLUTION: Must all be rounded to four decimal places 9e^19x = 16 ---> 0.0303 5(1+10^2x) = 8 ---> 0.006 the ones I don't know how to solve are: 10^(1-x) = 4x e^x - 12e^x -

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Must all be rounded to four decimal places 9e^19x = 16 ---> 0.0303 5(1+10^2x) = 8 ---> 0.006 the ones I don't know how to solve are: 10^(1-x) = 4x e^x - 12e^x -      Log On


   

Question 916604: Must all be rounded to four decimal places
9e^19x = 16 ---> 0.0303
5(1+10^2x) = 8 ---> 0.006
the ones I don't know how to solve are:
10^(1-x) = 4x
e^x - 12e^x - 1 = 0
Thank you
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
Must all be rounded to four decimal places 
9e%5E%2819x%29+=+16

ln%289e%5E%2819x%29%29+=+ln%2816%29

ln%289%29%2Bln%28e%5E%2819x%29%29=ln%2816%29

ln%289%29%2B19x=ln%2816%29

19x=ln%2816%29-ln%289%29

x=%28ln%2816%29-ln%289%29%29%2F19

x=0.0303

You got that one correct

5%281%2B10%5E%282x%29%29+=+8++%0D%0A%7B%7B%7B5+%2B+5%2A10%5E%282x%29=+8
5%2A10%5E%282x%29=3
log%285%29%2Blog%2810%5E%282x%29%29=log%283%29
log%285%29%2B2x=log%283%29
2x=log%283%29-log%285%29
x+=+%28log%283%29-log%285%29%29%2F2
x+=+-.1109

Oh! oh!, you missed that one.  Use "log" not "ln"

10%5E%281-x%29+=+4x

That one cannot be solved using algebra.  You can only
do it with a graphing calculator.  That's because if
a variable is both part of an exponent and also part od
something that is not an exponent, then there is no algebraic
method for solving it.  The calculator can do, but it
essentially does by trial and error, trying answers that get
closer and closer to solving it and giving the closest one
it can find. 

With a graphing calculator, the solution is

x = 0.6115 

-----------------------------

e%5Ex+-+12e%5Ex+-+1+=+0

The first two terms on the left are like terms,
(since both have ex ans 1-12 = -11)

1e%5Ex+-+12e%5Ex+-+1+=+0
-11e%5Ex+-+1+=+0
-11e%5Ex+=+1
e%5Ex+=+-1%2F11

There is no solution because "e" raised to any power is 
always positive and therefore can never equal a negative 
number.  Did you copy the problem wrong?

Edwin