Solving \(\displaystyle{x}^{{{\log{{\left({x}\right)}}}}}={\frac{{{x}^{{3}}}}{{{100}}}}\) How do I find the solution

Rex Maxwell

Rex Maxwell

Answered question


Solving xlog(x)=x3100
How do I find the solution to:
So I multiplied 100 both sides getting:
Now what should I do?

Answer & Explanation



Beginner2022-04-04Added 8 answers

I suppose log means log10? I'm not familiar with this sort of notation. Take logarithm on both sides, and you will get 2+log2x=3logx Substitute logx with t. And you get t23t+2=0, therefore (t1)(t2)=0. That should do it.
Marcos Boyer

Marcos Boyer

Beginner2022-04-05Added 12 answers

Since (log(x))2=log(xlogx)=log(x3100)=3log(x)2, we have (log(x))23log(x)+2=0. Hence, log(x)=2 and log(x)=1.
Therefore, x=100 atau x=10

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