If x^3x = 3x^4x, then find x.
You should move the terms to one side such that:
`x^(3x)- 3x^(4x) = 0`
You need to factor out `x^(3x) ` such that:
`x^(3x)(1 - 3x^(4x-3x)) = 0 => x^(3x)(1 - 3x^x) = 0 `
Since `x^(3x)!=0` , then only `1 - 3x^x = 0 => 3x^x = 1`
You need to divide by 3 both sides such that:
`x^x = 1/3`
You need to sketch the graphs of the function `y=x^x` and the graph of the function `y=1/3` such that:
Notice that the graphs do not intersect, hence, the given equation has no solution.
x^3x = 3x^4x
Divide both sides by x^3x
0 = (3x^4x) / (x^3x)
According to laws of exponents, when dividing powers, the exponents are subtracted.
(x^4x) / (x^3x) = x^(4x-3x) = x^x
Now we have the equation
0 = 3x^x
Divide both sides by 3.
0 = x^x
In order for a power to equal 0, the base would have to be 0 and the exponent would have to be a positive number. Since both the base and the exponent are x (and therefore the same number), this is impossible.
There is no solution.