Question 608917: ln(lne(exponent -x) =ln3
ln6x-ln(x+1)=ln4
lnx+3ln2=ln2/x
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! ln(lne(exponent -x) =ln3
lne^-x=-x (log of base raised to a power=power)
ln(-x)=ln(3)
-x=3
x=3
..
ln6x-ln(x+1)=ln4
ln6x-ln(x+1)-ln4=0
ln6x-(ln(x+1)+ln4)=0
place under single log
ln[6x/((x+1)*4)]=0
convert to exponential form:
e^0=6x/((x+1)*4)=1
6x=4x+4
2x=4
x=2
..
lnx+3ln2=ln2/x
I will assume last term is meant to be ln(2/x) instead of (ln2)/x which I am not able to solve.
lnx+3ln2=ln(2/x)
lnx+3ln2=ln2-lnx
2lnx+2ln2=0
place under single log
ln[x^2*2^2]=0
ln[4x^2]=0
convert to exponential form
e^0=4x^2=1
x^2=1/4
x=-1/2 (reject, x>0)
or
x=1/2
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