SOLUTION: (1/3) to the power of x = 6 to the 1-x power I have tried to solve this but I keep getting different answers. What are the correct steps and solution? Thank you

Question 433757: (1/3) to the power of x = 6 to the 1-x power
I have tried to solve this but I keep getting different answers. What are the correct steps and solution?
Thank you
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
(1/3) to the power of x = 6 to the 1-x power
=
Using natural logs
=
the log equiv of exponents
x* = (1-x)*
Find the nat logs of both
-.10986x = 1.79176(1-x)
-.10986x = 1.79176 - 1.79176x
1.79176x - 1.0986 = 1.79176
.693x = 1.79176
x =
x = 2.585
;
:
Check this with a calc
enter (1/3)^2.585, results .05843
enter 6^(1-2.585), results .05843; confirms our solution of x=2.585
RELATED QUESTIONS
Determine all the values of x for which: √x^(log10x)=100 (To be read as "the... (answered by Theo)

3x^3+x^2-3x-1=0 (The ^3 and ^2 and exponents) I have tried to factor and pull out (answered by stanbon)

This is the question: x to the 2nd power (x+1) -x (x to the 2nd power-1) =? I have... (answered by ankor@dixie-net.com)

i cant seem to Find the values of x in the following equation when i have tried i keep... (answered by Alan3354)

It says to solve the system of equations using the substitution method. x+y=1 3x+4y=1 (answered by elima)

1. What is the middle term in the expansion of (x-1/6)6th power? I tried puting both... (answered by mathchemprofessor)

(1/(x+2)^2)-(3/(x+2))=54 I can not figure out how to do this, i have tried... (answered by Alan3354)

In the expansion of (1 + 1/6x) to the power n, n belongs to N, n>8 the coeffient of x to... (answered by Fombitz)

This is the problem I need to solve for X 5-(8+3x)=2x+3 The answer is X= -6/5 (I am (answered by stanbon)