# How do you use the properties of logarithms to expand log_4 (5x)?

Oct 30, 2017

${\log}_{4} \left(5 x\right) = 1.16 + {\log}_{4} x$

#### Explanation:

${\log}_{4} \left(5 x\right) = {\log}_{4} 5 + {\log}_{4} x = \log \frac{5}{\log} 4 + {\log}_{4} x$

$= 1.16 \left(2 \mathrm{dp}\right) + {\log}_{4} x$

Properties used are :
  log_a (xy) = log x + log y and log_a x = log_10 x/log_10 a

${\log}_{4} \left(5 x\right) = 1.16 + {\log}_{4} x$ [Ans]