Lga(b)=c ⇒ b = a^c ; loga(b)=logc(a)/logc(b)
1) 2x+1=10^3=1000 x = 499,5
2) 4+6x= 10^(-1)=0,1 x= - 0,65
3) log5(5)/log5(1/5)=1/(-1)=x x= -1
4) = 6 ·3·log6 =18·log6 = log (6^18) (нет основание log)
5) = 2^(3log2(a)) = 2^log2(a³) = a³
6 logx = log(3·5/2) x =7,5
7) (x+4)/(x-3) = 8 ⇒ x+4=8x-24 x = 4
8) lg[(3x-11)·(x-27)]=3 3x² -81x-11x+297 = 10³
3x² - 92x -703 =0
x = [92 +/-√(92²+4·3·703)] /(2·3)
x = (92 +/-130)/6
x1 = 37
x2 = - 38/6 не уд., так как 3x- 11<0 x = 37<br> 9) log2{(x-5)·(x+2)] = 3 ⇒ x² -3x - 10 = 2³
x² - 3x - 18 = 0
x1= 6
x2 = -3 не уд, т.к. x-3 = -6<0 x= 6<br>