Question

解方程【对数】解方程：x^(-2/3)=4【√（2）+1】^x=【√（2）-1】】

Answer 1

x^(-2/3)=4

x^[(-2/3)*(-3/2)]=4^(-3/2)

x^1=4^(-3/2)

∴x=4^(-3/2)=1/8

……………………………………

【√（2）+1】^x=【√（2）-1】

∴x=lg[-1+√2]/lg[1+√2]

=lg[1/(1+√2)]/lg[1+√2]

=-lg[1+√2]/lg[1+√2]

=-1

至于换底公式,有性质以a为底b的对数,即log(a,b)=lgb/lga

log(a^m,b^n)=(n/m)log(a,b)