solve for x. log(x+12)=2log(x)

Question

campbell_st · Answer

well you can rewrite them using log laws

$$lof(x +12) = \log(x^2)$$

then raise each side as a power of the base

and you then need to solve 

x + 12 = x^2   

or x^2 - x - 12 = 0

now solve for x. 

hope it helps

lochana · Answer

that's right now you can factorize it easily

x^2 -x -12 = (x - 4)(x + 3)

x = 4 and -3

ganeshie8 · Answer

reject -3 because we need `x > 0` for the expression `log(x)` to be real

campbell_st · Answer

are you sure about x = -3



log (-3 + 12) = log((-3)^2)

I think you have to include x = -3 as a solution

campbell_st · Answer

it's always an interesting question...

ganeshie8 · Answer

$\log(x^2)$ is not necessarily same as $2\log x$

ganeshie8 · Answer

that holds only when $x$ is positive

ganeshie8 · Answer

attachment

gabrielah96 · Answer

thanks everyone!