Answer
$x=625$
Work Step by Step
Recall the power property of logarithms (pg. 462):
$\log_b{m^n}=n\log_b{m}$
Applying this property, we get:
$\log x^{1/2}+\log 4=2$
Next, recall the product property of logarithms (pg. 462):
$\log_b{mn}=\log_b{m}+\log_b{n}$
Applying this property to our last equation, we get:
$\log_{10}{\left(4x^{1/2}\right)}=2$
Now, recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition, we get:
$10^2=4x^{1/2}$
$100=4x^{1/2}$
$\frac{100}{4}=x^{1/2}$
$25=x^{1/2}$
$x=25^2$
$x=625$
We confirm that the answer works:
$\frac{1}{2}\log 625+\log 4=2$
$\frac{1}{2}*2.8+0.6=2$
$2=2$
