Question

已知y=2^m+1,x=3+16^m,试用y的代数式表示x

Answer 1

y=2^m+1,

2^m=y-1

m=log2[y-1]

把m带入x的表达式得

x=3+16^m

=3+16^{l0g2[y-1]}

=3+2^{4log2[y-1]}

=3+2^{log2[y-1]^4}

=3+(y-1)^4

所以 x=(y-1)^4+3