Answer
$x\approx 2.1240$
Work Step by Step
Recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation (with $b=4, y=x, x=19$), we get:
$\log_{4}{19}=x$
Next, recall the change of base formula (pg. 464):
$\log_{b}{m}=\frac{\log_{c}{m}}{\log_{c}{b}}$
Applying this property to our last equation, we get:
$\log_{4}{19}=x$
$\dfrac{\log 19}{\log 4}=x$
Use a calculator to obtain:
$x\approx 2.1240$
We confirm that the answer works:
$4^{2.1240}\approx19$
