How do you solve 10^(x+2) - 12 = 22 10x+212=22 and find any extraneous solutions?

1 Answer
Jul 22, 2016

The Soln. is x=-0.4685x=0.4685

Explanation:

10^(x+2)-12=22 rArr 10^(x+2)=12+22=3410x+212=2210x+2=12+22=34

rArrlog_(10)10^(x+2)=log_(10)34log1010x+2=log1034

rArr (x+2)log_(10)10=1.5315(x+2)log1010=1.5315..................[Using LogTable]

rArr (x+2)*1=1.5315(x+2)1=1.5315

rArr x+2=1.5315x+2=1.5315

rArr x=1.5315-2x=1.53152

rArr x=-0.4685x=0.4685 is the Soln.