Solve for x using properties of logarithms: ln(9)+ln(x+2)=2ln(x+2) ?

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Answer 1 · 2018-02-28T14:41:12

#x=7#

#ln(9)+1n(x+2)=2ln(x+2)#

Subtract #2ln(x+2)# from both sides:

#ln(9)+1n(x+2)-2ln(x+2)=0#

Simplify:

#ln(9)-1n(x+2)=0#

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

Hence:

#ln(9)-1n(x+2)=0=>ln(9/(x+2))=0#

Raising the base #e# to these powers:

#e^(ln(9/(x+2))=e^0#

#9/(x+2)=1#

#x=7#

Substituting in original equation:

#ln(9)+1n((7)+2)=2ln((7)+2)#

#ln(9)+1n(9)=2ln(9)#

#2ln(9)=2ln(9)#