# How do you find the limit of ( ln(4x) - ln(x) ) / ( ln(x) ) as x approaches 1?

Apr 20, 2015

Using the property of logarithm:

$\log \left(a b\right) = \log a + \log b$ (with $a , b > 0$)

${\lim}_{x \rightarrow 1} \frac{\ln \left(4 x\right) - \ln \left(x\right)}{\ln \left(x\right)} = {\lim}_{x \rightarrow 1} \frac{\log 4 + \log x - \log x}{\log} x =$

$= {\lim}_{x \rightarrow 1} \log \frac{4}{\log} x = \infty$.

Apr 21, 2015