Daniel J Smith Custom TMUA Set A Paper 1 · Question 2

For non-zero real numbers $a$ and $b$ , consider the equation

\log_3(x-a)=\log_3x+b

The number of real solutions $x$ depends on $a$ and $b$ .

Which of the following is correct?

AExactly one real solution if

a(1-3^b)>0

and no real solutions if

a(1-3^b)<0

BExactly one real solution if

a(1-3^b)<0

and no real solutions if

a(1-3^b)>0

CExactly two real solutions if

a(1-3^b)>0

and none otherwise

DNo real solutions if

ab>0

and exactly one real solution if

ab<0

EThe equation always has exactly one real solution for all non-zero

a

and

b

examday