Question

16^x-1=216
решить уравнение

Answer 1

16^(x-1)=216
2^4(x-1)=216
log2(2^4(x-1))=log2(216)
4(x-1)log2(2)=log2(2^3*3^3)=log2(2^3)+log2(3^3)=3log2(2)+3log2(3)=3(1+log2(3))
4(x-1)=3(1+log2(3))
x-1 = 3/4 (1+log2(3))
x = 3/4 (1+log2(3)) +1