Answer
$x=5$
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:
$\log x^2+\log 4=2$
Next, recall the product property of logarithms (pg. 462):
$\log_b{mn}=\log_b{m}+\log_b{n}$
Applying this property to our equation, we get:
$\log_{10} 4x^2=2$
Now, recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation (with $b=10, y=2, x=4x^2$), we get:
$10^{2}=4x^2$
$100/4=x^2$
$25=x^2$
$x=\sqrt{25}$
$x=5$
We confirm that the answer works:
$2\log 5+\log 4=2$
$\log 5^2+\log 4=2$
$\log{(5^2\cdot4)}=2$
$\log{100}=2$
$\log{10^2}=2$
$2=2$
