Question

LoJao(37-3八):log 20 (3rniay)

Answer 1

Hello,
if the question is to solve the equation:

1) log must exist:
a)==>2r²-27>0==>(r-√(27/2))(r+√(27/2))==> outside the roots
r<-√(27/2) or r>√(27/2)
b)==>3r²+12r>0 ==>3r(r+4)>0 ==>outside the roots
r>0 or r<-4
==>r<-4 or r>√(27/2)=3.6742...

If this is realized:
2r-27=3r²+12r
==>r²+12r+27=0
Δ=12²-4*27=36=6²
r=(-12+6)/2=-3 or r=(-12-6)/2=-9

One solution r=-9

Proof
 $log_{20}(2*(-9)^2-27)= log_{20}135$

 $log_{20}(3*(-9)^2+12*(-9))= log_{20}135$