We report about nonlinear growth of x-ray emission intensity emitted from plasma generated by femtosecond petawatt laser pulses irradiating stainless steel foils. X-ray emission intensity increases as ∼ I ^4.5 with laser intensity I on a target. High spectrally resolved x-ray emission from front and rear surfaces of 5 μm thickness stainless steel targets were obtained at the wavelength range 1.7-2.1 Å, for the first time in experiments at femtosecond petawatt laser facility J-KAREN-P. Total intensity of front x-ray spectra three times dominates to rear side spectra for maximum laser intensity I ≈ 3.210²¹ W/cm². Growth of x-ray emission is mostly determined by contribution of bremsstrahlung radiation that allowed estimating bulk electron plasma temperature for various magnitude of laser intensity on target.