Question on solving a Logarithmic equation

Question

$\ln(x+3)^{\frac{1}{2}} + \ln (4x-3)^{\frac{1}{2}} = \ln (5)$

So I understand that in order to solve this log function, I would have to square the square roots to simplify the equation.

But how does the number $e$ come into play?

Answer 1

Hint:

$$\log A^{1/2}=\frac12\log A\;,\;\;A>0$$

$$\log A+\log B=\log(AB)$$

Answer 2

No you dont have to square the square roots.

$ln(A)+ln(B)=ln(C)$

But we know that $ln(A)+ln(B)=ln(AB)$

So:

$ln(AB)=ln(C)$

$e^{AB}=e^{C}$ (Note: This is where e comes into play)

But we know that:

$a^b=a^c$ $b=c$

Therefore we can say that :

$e^{AB}=e^{C}$

$(AB)=C$