Simplify. Enter the result as a single logarithm with a coefficient of 1. log_3(4x^3)−log_3(5x^9) ?

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Answer 1 · 2018-03-06T02:05:39

The simplified result is #log_3(4/(5x^6))#

#log_x(a)-log_x(b)=log_x(a/b)#

Here's the actual problem (I color-coded some parts so they are easier to follow):

#color(white)=log_3(color(red)(4x^3))−log_3(color(blue)(5x^9))#

#=log_3(color(red)(4x^3)/color(blue)(5x^9))#

#=log_3(color(red)(4color(black)cancel(color(red)(x^3)))/color(blue)(5color(black)cancel(color(blue)(x^9)))^color(blue)6)#

#=log_3(color(red)4/color(blue)(5x^6))#