Question

1. 4^(х+3)/х + 4^(2х+3)/х = 320

2. 0,8^(0,8-5х) = 0,5√5

Answer 1

$3)0,8^{0,8-5x} =0,5\sqrt{5}\\\\(\frac{4}{5})^{0,8-5x}=\sqrt{\frac{1}{4} *5}\\\\(\frac{4}{5} )^{0,8-5x}=(\frac{5}{4})^{\frac{1}{2} }\\\\(\frac{5}{4})^{5x-0,8}=(\frac{5}{4})^{0,5}\\\\5x-0,8=0,5\\\\5x=1,3\\\\x=0,26\\\\4)4^{\frac{x+3}{x} }+4^{\frac{2x+3}{x} } =320\\\\4^{1}*4^{\frac{3}{x} }+4^{2}*4^{\frac{3}{x}}=320\\\\4*4^{\frac{3}{x} }+16*4^{\frac{3}{x} } =320\\\\20*4^{\frac{3}{x} }=320\\\\4^{\frac{3}{x} }=16\\\\4^{\frac{3}{x} }=4^{2}\\\\\frac{3}{x}=2\\\\x=1,5$