How do you solve #log_7 9-log_7(-3x)=2#?

1 Answer
Jul 17, 2016

Answer:

#x=-3/49#

Explanation:

Using the #color(blue)"laws of logarithms"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(logx-logy=log(x/y))color(white)(a/a)|))) ........ (A)#

#color(red)(|bar(ul(color(white)(a/a)color(black)(log_b x=nhArrx=b^n)color(white)(a/a)|))) ........ (B)#

Using (A): #log_7 9-log_7(-3x)=log_7(9/(-3x))#

#=log_7(3/(-x))#

Using (B) : #log_7(3/(-x))=2#

#rArr3/(-x)=7^2=49#

#rArr-49x=3rArrx=-3/49#