Answer
$x=500$
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:
$\log 4+\log x^2=6$
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:
$\log 4+\log x^2=6$
$\log_{10} 4x^2=6$
Now, recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition, we get:
$10^6=4x^2$
$\frac{10^6}{4}=x^2$
$\sqrt{\frac{10^6}{4}}=x$
$\frac{10^3}{2}=x$
$\frac{1000}{2}=x$
$x=500$
We confirm that the answer works:
$\log 4+2\log 500=6$
$0.6+2*2.7=6$
$6=6$
