How do you evaluate #2 ln x -3(ln x^2 + ln x)#?

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Answer 1 · 2017-11-28T08:34:44

#-7lnx=ln(x^(-7))#

Step 1:
Using the addition rule that #ln(a)+ln(b)=ln(ab)#

#lnx^2+lnx=lnx^3#

#2lnx-3lnx^3#

Step 2:
Using the power rule that #kln(x)=ln(x^k)#

#3ln(x^3)=3(3lnx)=9lnx#

#2lnx-9lnx=-7lnx#

Step 3:
Using the power rule again.

#-7lnx=ln(x^(-7))#

Answer 2 · 2017-11-28T08:42:33

#-7lnx#

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

#•color(white)(x)logx^nhArrnlogx#

#rArr2lnx-3lnx^2-3lnx#

#=2lnx-6lnx-3lnx#

#=-7lnx#