How do you simplify #log_ax - log_a9 - log_a(x^2+1) + log_a5#?

1 Answer
Jim G.
Apr 23, 2016

#log_a((5x)/(9(x^2+1)))#

Explanation:

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

#• logx + logy hArr log(xy)#

#• logx - logy hArr log(x/y) #

rewriting the above expression as follows:

# log_a x + log_a 5 -(log_a 9 + log_a(x^2+1))#

#rArr log_a(5x) - ( log_a (9(x^2+1))#

# = log_a ((5x)/(9(x^2+1)))#

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