Question

solve the equation. log 3x + log x = 6
x = (round to the nearest whole number as needed.)

Explanation:

Step1: Use log property

By the property $\log a+\log b = \log(ab)$, we have $\log(3x\cdot x)=6$, so $\log(3x^{2}) = 6$.

Step2: Convert to exponential form

If the base of the logarithm is 10 (common - log), then in exponential form $10^{6}=3x^{2}$. Since $10^{6}=1000000$, the equation becomes $1000000 = 3x^{2}$.

Step3: Solve for $x^{2}$

Divide both sides of the equation $1000000 = 3x^{2}$ by 3: $x^{2}=\frac{1000000}{3}\approx333333.33$.

Step4: Solve for $x$

Take the square - root of both sides. Since $x>0$ (because we have $\log x$ in the original equation and the argument of a logarithm must be positive), $x=\sqrt{\frac{1000000}{3}}\approx577$.

Answer:

577