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

1 Answer
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)