Question 658852: If x^3x = (3x)^4x, then find the value of x.
Answer by Shana-D77(132)   (Show Source):
You can put this solution on YOUR website! If x^3x = (3x)^4x, then find the value of x.
There's a lot going on here. Firs, let's use an exponent rule:
x^3x = (x^3)^x and
(3x)^4x = ((3x)^4)^x
So we have:
(x^3)^x = ((3x)^4)^x
Take the log of both sides (remembering log rules):
x log x^3 = x log (3x)^4 ( log rules - email for more info on this if it doesn't make sense)
Divide both sides by x log:
x^3 = (3x)^4
x^3 = (3^4)(x^4) (more exponent rules)
x^3 = (81)(x^4)
(x^3)/(x^4) = 81 (divided both sides by x^4)
1/x = 81 (even more exponent rules)
x = 1/81
|
|
|
