# What are possible values of x if ln(x-4) +ln(3) <=0?

May 14, 2018

#### Answer:

Possible values of $x$ are given by $4 < x \le \frac{13}{3}$

#### Explanation:

We can write $\ln \left(x - 4\right) + \ln 3 \le 0$ as

$\ln \left(3 \left(x - 4\right)\right) \le 0$

graph{lnx [-10, 10, -5, 5]}

Now as $\ln x$ is a function which always increases as $x$ increases (graph shown above) as also that $\ln 1 = 0$, this means

$3 \left(x - 4\right) \le 1$

i.e. $3 x \le 13$

and $x \le \frac{13}{3}$

Observe that as we have $\ln \left(x - 4\right)$ domain of $x$ is $x > 4$

Hence possible values of $x$ are given by $4 < x \le \frac{13}{3}$