If #2Log_a x + Log_a(ax) + 3Log_a(a^2x) = 0 #, Find #x#... ?

1 Answer
e52fa787 · mason m
Aug 30, 2017

#x=a^(-7/6)#

Explanation:

This will use the rules to expand the given logarithms, then combine the like terms:

  • #log(AB)=log(A)+log(B)#
  • #log(A^B)=Blog(A)#

#2log_a(x)+log_a(ax)+3log_a(a^2x)#

#=2log_a(x)+log_a(a)+log_a(x)+3(log_a(a^2)+log_a(x))#

#=2log_a(x)+log_a(a)+log_a(x)+3(2log_a(a)+log_a(x))#

#=2log_a(x)+log_a(a)+log_a(x)+6log_a(a)+3log_a(x)#

#=6log_a(x)+7log_a(a)#

#=6log_a(x)+7 = 0#

#:. log_a(x)=-7/6#

#x=a^(-7/6)#

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