#### Answer

$x=10$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
\log x+\log x^2=3
,$ use the properties of logarithms to simplify the given expression. Then convert to exponential form.
$\bf{\text{Solution Details:}}$
Using the Power Rule of Logarithms, which is given by $\log_b x^y=y\log_bx,$ the equation above is equivalent
\begin{array}{l}\require{cancel}
\log x+2\log x=3
.\end{array}
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
(1+2)\log x=3
\\\\
3\log x=3
\\\\
\log x=\dfrac{3}{3}
\\\\
\log x=1
.\end{array}
Since $\log x=\log_{10} x,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
\log_{10} x=1
.\end{array}
Since $y=b^x$ is equivalent to $\log_b y=x,$ the exponential form of the equation above is
\begin{array}{l}\require{cancel}
10^1=x
\\\\
x=10
.\end{array}