Question

1. ㏒(x²+4) = 2 + ㏒x - ㏒20
2. ㏒x²+1 - 2log x = 1

Please solve in a comprehensible manner. thanks

Answer 1

Step-by-step explanation:

1) log(x^2+4)=2+logx-log20

log(x^2+4)=log 100+logx-log 20

log(x^2+4)=log(100×x/20)

log(x^2+4)=log(5x)

x^2+4=5x

x^2-5x+4=0

x^2-4x-1x+4=0

(x-4)(x-1)=0

X=4 or 1

2)LHS=log x^2+1-2logx

=logx^2+log 10-logx^2

=log(x^2×10/x^2)

=log 10

=1=RHS. "H.P"

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