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

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#log_(4)sqrt(x^3)#

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Answer 1 · 2017-02-12T16:47:37

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

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#