Question

log5 x - log25 x + log625 x = 3/4

Answer 1

$\displaystyle\bf\\ODZ:x>0\\\\\log_{5} x-\log_{25} x+\log_{625} x=\dfrac{3}{4} \\\\\\\log_{5} x-\log_{5} x^{\frac{1}{2} } +\log_{5}x^{\frac{1}{4} } =\dfrac{3}{4} \\\\\\\log_{5} x-\dfrac{1}{2} \log_{5} x+\dfrac{1}{4} \log_{5} x=\dfrac{3}{4} \\\\\\\dfrac{3}{4} \log_{5} x=\dfrac{3}{4} \\\\\\\log_{5} x=1\\\\\\\boxed{x=5}$