# Exercise ID317

Algebra → Logarithm → Logarithm equations
[Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 7] [Number of characters: 0]

Evaluate the following expression:

$\frac{\left({\mathrm{log}}_{\sqrt[3]{27}}\left(3\right)+{\mathrm{log}}_{\sqrt[49]{5}}\left(25\right)\right)×\left({\mathrm{log}}_{\sqrt[4]{81}}\left(9\right)-{\mathrm{log}}_{\sqrt[9]{8}}\left(4\right)\right)}{3+{5}^{\frac{1}{{\mathrm{log}}_{16}\left(25\right)}}×{5}^{{\mathrm{log}}_{5}\left(3\right)}}=\phantom{\rule{0ex}{0ex}}$

$\frac{\left({\mathrm{log}}_{\sqrt[3]{{3}^{3}}}\left(3\right)+{\mathrm{log}}_{{5}^{\frac{1}{49}}}\left({5}^{2}\right)\right)×\left({\mathrm{log}}_{\sqrt[4]{{9}^{2}}}\left(9\right)-{\mathrm{log}}_{\sqrt[9]{{2}^{3}}}\left({2}^{2}\right)\right)}{3+{5}^{{\mathrm{log}}_{25}\left(16\right)}×3}=\phantom{\rule{0ex}{0ex}}$ $\frac{\left({\mathrm{log}}_{3}\left(3\right)+49{\mathrm{log}}_{5}\left({5}^{2}\right)\right)×\left({\mathrm{log}}_{{9}^{\frac{2}{4}}}\left(9\right)-{\mathrm{log}}_{{2}^{\frac{3}{9}}}\left({2}^{2}\right)\right)}{3+{5}^{{\mathrm{log}}_{{5}^{2}}\left(16\right)}×3}=\phantom{\rule{0ex}{0ex}}$ $\frac{\left({\mathrm{log}}_{3}\left(3\right)+2×49{\mathrm{log}}_{5}\left(5\right)\right)×\left(2{\mathrm{log}}_{9}\left(9\right)-3×2{\mathrm{log}}_{2}\left(2\right)\right)}{3+{5}^{\frac{1}{2}{\mathrm{log}}_{5}\left(16\right)}×3}=\phantom{\rule{0ex}{0ex}}$ $\frac{\left(1+2×49×1\right)×\left(2×1-3×1\right)}{3+{5}^{{\mathrm{log}}_{5}\left({16}^{\frac{1}{2}}\right)}×3}=\phantom{\rule{0ex}{0ex}}$ $\frac{99×\left(-4\right)}{3+\sqrt{16}×3}=\phantom{\rule{0ex}{0ex}}$ $\frac{99×\left(-4\right)}{3+4×3}=\phantom{\rule{0ex}{0ex}}$ $-\frac{132}{5}\phantom{\rule{0ex}{0ex}}$
$-\frac{132}{5}\phantom{\rule{0ex}{0ex}}$