Algebra is cool

Algebra Level 2

$\large \ln(x-2) + \ln(2x-3) = 2\ln(x) \quad,\quad x = \ ?$

10 8 6 3

1 solution

The Adammz
Sep 1, 2015

$\ln { (x-2) } +\ln { (2x-3) } =2\ln { (x) }$

$\ln { [(x-2)(2x-3)] } =\ln { (x^{2}) }$

$2x^2-7x+6=x^2$

$x^2-7x+6=0$

$(x-1)(x-6)=0$

$x=1$ or $x=6$

Edit again: When $x=1$ , $\ln { (x-2) }$ would be invalid. So x must be equal to 6.

You should mention that the domain is restricted such that x>2 because of the ln(x-2) term. Therefore there is only the one solution x=6.

Jonathan Hocker - 5 years, 9 months ago

Okay. Edited.

The AdamMZ - 5 years, 9 months ago

The answer is 6. This is not because there is only one option. This is because the other option of $x=1$ is invalid. $\log(x-2)$ is not a real number for $x=1$

Janardhanan Sivaramakrishnan - 5 years, 9 months ago

Oh, okay. Got it.

The AdamMZ - 5 years, 9 months ago

What is this in????

Thakur Singh - 4 years, 8 months ago

The problem would be more interesting if the extra root, that is 1, were included as an option for an answer. And even better if both were included in one of the answers.

Marta Reece - 3 years ago

Algebra is cool

1 solution

0 pending reports