解方程2^n+1+4^n=48

解方程：2ⁿ⁺¹+4ⁿ=48

解：原式=2²·2ⁿ+(2²)ⁿ=48文章源自趣课程-https://www.qukecheng.com/1732.html

=2·2ⁿ+(2ⁿ)²-48=0文章源自趣课程-https://www.qukecheng.com/1732.html

=(2ⁿ+8)(2ⁿ-6)=0文章源自趣课程-https://www.qukecheng.com/1732.html

2ⁿ=-8（负数舍去）或2ⁿ=6文章源自趣课程-https://www.qukecheng.com/1732.html

n=log₂⁶文章源自趣课程-https://www.qukecheng.com/1732.html

^{所以n等于以2为底数6的对数。}文章源自趣课程-https://www.qukecheng.com/1732.html

文章源自趣课程-https://www.qukecheng.com/1732.html

文章源自趣课程-https://www.qukecheng.com/1732.html

文章源自趣课程-https://www.qukecheng.com/1732.html 文章源自趣课程-https://www.qukecheng.com/1732.html