Question

Help, please the product of x and y

Answer 1

`xy \\\\=\left(\log_(5\sqrt 5) ~125 \right)\left(\log_(2\sqrt 2) ~64 \right)\\\\=\left(\log_(5\sqrt 5) ~5^3 \right)\left(\log_(2\sqrt 2)~2^6 \right)\\\\=\left(3\log_(5\sqrt 5) ~5 \right)\left(6\log_(2\sqrt 2) ~2 \right)\\\\=\left( 18 \cdot (\ln5)/(\ln\left(5\sqrt 5\right)) \cdot (\ln 2)/( \ln \left( 2 \sqrt 2 \right))\right)\\\\`

`=\left( 18 \cdot (\ln5)/(\ln\left(5^(\tfrac 32)\right)) \cdot (\ln 2)/( \ln \left( 2^(\tfrac 32) \right))\right)~~~~~~~~~~~;\left[\sqrt a = a^(\tfrac 12)~~ \right]\\\\=\left( 18 \cdot (\ln5)/(\tfrac 32\ln5^) \cdot (\ln 2)/(\tfrac 32 \ln 2 )\right)\\\\\\=18 \cdot \frac 23 \cdot \frac 23 \\\\=\frac{72}9\\\\=8`