a^x-2*2^x大于0,已知a大于1請(qǐng)問x取值?

熱心網(wǎng)友

a^x2^(x+1),兩邊取對(duì)數(shù):xLga(x+1)Lg2,x(Lga-Lg2)Lg2(1)當(dāng)a2,x系數(shù)為正,xLg2/(Lga-Lg2)(2)當(dāng)a<2,.......負(fù),x<...........(3)當(dāng)a=2,無解

熱心網(wǎng)友

a^x-2*2^x大于0,已知a大于1請(qǐng)問x取值? 解：a^x-2*2^x大于0即a^x-2^(x+1)0a^x2^(x+1)兩邊取常用對(duì)數(shù),得xlga(x+1)lg2xlga-xlg2lg2x(lga-lg2)lg2xlg(a/2)lg2(1)當(dāng)a2時(shí),lg(a/2)0,xlg2/Lg(a/2)；(2)當(dāng)a<2時(shí),lg(a/2)<0,x