Question

HELP ASAP!!!!!
Pre-calculus

Answer 1

`xy=log_5\sqrt5(125)\cdot\log_(2\sqrt2)64\\\\xy=(\log_5125)/(\log_5 5\sqrt5)\cdot(\log_264)/(\log_22\sqrt2)\\\\xy=\frac{3}{\log_55^{\tfrac{3}{2}}}\cdot\frac{6}{\log_22^{\tfrac{3}{2}}}\\\\xy=(3)/((3)/(2))\cdot(6)/((3)/(2))\\\\xy=3\cdot(2)/(3)\cdot6\cdot(3)/(2)\\\\xy=18`

Answer 2

The product of x and y is 8.

Explanation:

It is given that

`x=\log_(5√(5))\left(125\right)`

`y=\log_(2√(2))\left(64\right)`

We need to find the product of x and y.

`x\cdot y=\log_(5√(5))\left(125\right)\cdot\log_(2√(2))\left(64\right)`

It can be written as

`xy=\log_(5√(5))\left(5√(5)\right)^2\cdot\log_(2√(2))\left(2√(2)\right)^4`

Using the properties of logarithm, we get

`xy=2\cdot 4`
`[\because log_aa^x=x]`

`xy=8`

Therefore the product of x and y is 8.