How to solve the log Equation

Question

I tried to solve the Equation but unfortunately Whatever I try, I can't solve the Equation

$$100^{\log x}=3x^3$$

I would recommend solving for $\log x$ after taking logs of both sides. — Karl Kroningfeld, Sep 09 '13 at 06:51

score 5 · Accepted Answer · answered Sep 09 '13 at 06:27

5

$$100^{\log x}=3x^3$$ $$(10^2)^{\log x}=3x^3$$ $${(10^{\log x})}^2=3x^3$$ $$x^2=3x^3$$ $$3x^3-x^2=0$$ $$x^2(3x-1)=0$$ $$x=0,\frac{1}{3}$$

But, $x$ must be positive, so the only solution is $\frac{1}{3}$

answered Sep 09 '13 at 06:27

NightRa

1

With appropriate caveats, of course, about the "solution" $x = 0$. – Sep 09 '13 at 06:31

1 Answers1