I need to rewrite the expression as a single logarithm. How can I do that? Thanks!

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1 Answer
Jim G.
Nov 9, 2017

#ln[(root(3)(x)(x-3)^4)/(sqrt((x+3)^3)]]#

Explanation:

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

#•color(white)(x)logx^nhArrnlogx#

#•color(white)(x)logx+logyhArrlog(xy)#

#•color(white)(x)logx-logyhArrlog(x/y)#

#rArr1/3lnx+4[ln(x-3)-ln(x+3)^(3/8)]#

#=1/3lnx+4[ln((x-3)/((x+3)^(3/8)))]#

#=1/3lnx+4ln[((x-3))/((x+3)^(3/8))]#

#=1/3lnx+ln[(x-3)/(x+3)^(3/8)]^4#

#=1/3lnx+ln[(x-3)^4/(x+3)^(3/2)]#

#=lnx^(1/3)+ln[(x-3)^4/(x+3)^(3/2)]#

#=ln[(x^(1/3)(x-3)^4)/(x+3)^(3/2)]]#

#=ln[(root(3)(x)(x-3)^4)/sqrt((x+3)^3)]#

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