# JavaScript, 51 bytes

    f=(a,b,c,h,i,j)=>(l=Math.log)(a)*b**c-l(h)*i**j>1e-8

<s>Surprisingly, the test cases doesn't show any floating-point error. I don't know if it ever does at this size.</s>

This just compares the logarithm of the numbers.

Equality tolerance is equal to `1e-8`.