Solve for $x$ :
\[
x=10^{7 \log _{10} 6-\log _{10} 3}
\]
\[
x=
\]

Note: Your answer must be exact and in simplest form.

Answer

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Answer

So, the solution to the equation is $x=\boxed{\frac{6^7}{3}}$

Steps

Step 1 ：Given the equation $x=10^{7 \log _{10} 6-\log _{10} 3}$

Step 2 ：We can simplify the equation using the properties of logarithms

Step 3 ：Using the property $a^{log_a b} = b$, we can rewrite the equation as $x = 10^{7 \log _{10} 6} / 10^{\log _{10} 3}$

Step 4 ：Further simplifying, we get $x = (10^{\log _{10} 6})^7 / 3$

Step 5 ：Finally, we get $x = 6^7 / 3$

Step 6 ：So, the solution to the equation is $x=\boxed{\frac{6^7}{3}}$