How do you condense #4\ln ( 3x + 5) - 2\ln x - \frac { 1} { 3} \ln ( 2x + 3)#?

2 Answers
Binayaka C.
Jun 1, 2017

# ln ((3x+5)^4/(x^2*root(3)(2x+3)))#

Explanation:

# 4 ln (3x+5) -2 ln(x) -1/3 ln(2x+3) # or

# ln (3x+5)^4 - ln(x)^2 - ln(2x+3)^(1/3) # or

# ln ((3x+5)^4/(x^2*root(3)(2x+3)))# [Ans]

Jim G.
Jun 1, 2017

#ln((3x+5)^4/(x^2(2x+3)^(1/3)))#

Explanation:

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

#color(red)(bar(ul(|color(white)(2/2)color(black)(logx^nhArrnlogx)color(white)(2/2)|)))" and "#

#color(red)(bar(ul(|color(white)(2/2)color(black)(logx+logyhArrlog(xy);logx-logyhArrlog(x/y))color(white)(2/2)|)))#

#rArr4ln(3x+5)-2lnx-1/3ln(2x+3)#

#=ln(3x+5)^4-lnx^2-ln(2x+3)^(1/3)#

#=ln(3x+5)^4-ln(x^2(2x+3)^(1/3))#

#=ln((3x+5)^4/(x^2(2x+3)^(1/3)))#

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