If 2log4x−log4(4x+3)=−1, then log2x=....
Explanation
The requirement for logarithm logab is that a>0. Therefore
2log4x−log4(4x+3)=−1
Where the value x>0.
Determine the value of x
2log4x−log4(4x+3)=−1
log4x2−log4(4x+3)=log44−1
log44x+3x2=log441
4x+3x2=41
4x2=4x+3
4x2−4x−3=0
Factor
(2x+1)(2x−3)=0
2x+1=0∪2x−3=0
x=−21∪x=23
Since the requirement is x>0, then x=23 satisfies. Therefore
log2x=log223
log2x=log23−log22
log2x=log23−1