If log102,log10(2x–1)andlog10(2x+3) are in AP, then x is equal to:
log25
log2-1
log215
log52
Explanation for the correct option.
As log102,log10(2x–1)andlog10(2x+3) are in AP, so
2log10(2x–1)=log102+log10(2x+3)⇒(2x–1)2=2(2x+3).....1
Let 2x=y, so the equation 1, will be
y-12=2y+3⇒y2-2y+1=2y+6⇒y2-4y-5=0⇒y2+y-5y-5=0⇒y-5y+1=0⇒y=5or-1
As exponential fn, cannot be negative, so 2x=y=5.
Therefore, x=log25
Hence, option A is correct.