Question

高一对数方程解方程 x^log2(x)=32x^4 x的log2(x)次方=32*x的4次方x^log2(x)=32x^

Answer 1

x^log2(x)=32x^4

两边同时取以2为底的对数,则有log2[x^log2(x)]=log2(32x^4)

log2(x)*log2(x)=log2(32)+log2(x^4)

[log2(x)]²=log2(2^5)+4log2(x)

[log2(x)]²=5+4log2(x)

[log2(x)]²-4log2(x)-5=0

[log2(x)-5][log2(x)+1]=0

log2(x)-5=0或log2(x)+1=0

log2(x)=5或log2(x)=-1

∴log2（x）=5=log2（2^5）=log2(32),x=32

或log2(x)=-1=log2(1/2),x=1/2

x=32或x=1/2