How do you expand this logarithm? log_(4)sqrt(x^3)

log_(4)sqrt(x^3)

1 Answer
Feb 12, 2017

log_4root(3)x=1/3log_4x=1/3logx/log4=0.5537logx

Explanation:

As #log_aroot(n)x=log_a(x)^(1/n)=1/nlog_ax,

As such log_4root(3)x=log_4(x)^(1/3)=1/3log_4x

but as log_ab=logb/loga

log_4root(3)x=1/3logx/log4=1/3logx/0.6021=0.5537x