I don't know how to put : $9x\cdot 10^x-8\cdot 10^x > 10^7$ in the form : $b\cdot e^b > a$ so that i can use the Lambert-W function to solve this inequality Any ideas ?
2026-03-27 04:22:24.1774585344
Inequation + Lambert-W function
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$$(9x-8)10^x>10^7$$
Shift by $8/9$
$$9y\,10^y10^{8/9}>10^7$$
Scale by $\ln10$,
$$\frac{9z}{\log10}e^z10^{8/9}>10^7$$
Divide
$$ze^z>\frac{\log10}{9}10^{7-8/9}$$