How do you expand #ln(uv^6)^5#?

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Answer 1 · 2016-09-24T22:55:39

#5lnu+30lnv#

#ln(uv^6)^5#

Use log rule #logx^a=alogx#
#5lnuv^6#

Use log rule #logxy=logx+logy#
#5(lnu+lnv^6)#

Again use log rule #logx^a=alogx#
#5(lnu+6lnv)#

Distribute
#5lnu+30lnv#

OR
#ln(uv^6)^5#

Use exponent rule #(x^a)^b=x^(ab)#
#ln(u^5v^30)#

Use log rule #logxy=logx+logy#
#lnu^5+lnv^30#

Use log rule #logx^a=alogx#
#5lnu+30lnv#