Question

Find the value of x if log (x-6)=2,use log with base 3

Answer 1

Answer:

log

x+1

(x

2

+x−6)

2

=4

(x+1)

4

=(x

2

+x−6)

2

⇒2x

3

+17x

2

+16x−35=0

⇒(x−1)(2x

2

+19x+35)=0

⇒(x−1)(2x+5)(x+7)=0

⇒x=1,−7,−

2

5

Now, from the given equation it follows that

x+1>0,x+1



=1,x

2

+x−6



=0

x>−1,x



=0,x



=−3,x



=2

⇒x∈(−1,0)∪(0,2)∪(2,∞)

So,x=1 lies in this range.

So, required value =2