Question

dados log2=0 30 log3=0 48 e log5=0 70 resolva a equação 5^2x - 7x5^x + 6 =0

Answer 1

          $5^{2x} -7x 5^{x} +6=0 \\ \\ (5^x)^2-7(5^x) + 6=0 \\ \\ 5^x = z \\ \\ z^2-7z+6=0 \\ (z-1)(z-6)=0 \\ z1=1 \\ z2=6 \\ \\ 5^x= 1 \\ 5^x=5^0 \\ x1=0 \\ \\ 5^x=6 \\ xlog5=log6=log2+log3 \\ x= \frac{log2+log3}{log5} \\ x= \frac{0,30+0,48}{0,7} \\ x2=1,1143$
 
                          S = {0; 1,1143}