Two similar logarithmic equations:

1) $\displaystyle x^{lgx}=1000x^2$

2) $\displaystyle x^{\frac{lgx+7}{4}}=10^{lgx+1}$

I tried solving the first one:

$\displaystyle x>0;$

I tried to write the first exponent in the base x, so that I could apply the rule $\displaystyle a^{loga(b)}=b$:

$\displaystyle x^{\frac{logx(x)}{logx(10)}}=1000x^2$

But it didn't work, because I got in the exponent $\displaystyle \frac{1}{logx(10)}$

How do I solve these?