Question

HELP ASAP!!!!! Pre-calculus

Answer 1

$xy=\log_{5\sqrt5}{125}\cdot\log_{2\sqrt2}64\\\\xy=\dfrac{\log_5125}{\log_5 5\sqrt5}\cdot\dfrac{\log_264}{\log_22\sqrt2}\\\\xy=\dfrac{3}{\log_55^{\tfrac{3}{2}}}\cdot\dfrac{6}{\log_22^{\tfrac{3}{2}}}\\\\xy=\dfrac{3}{\dfrac{3}{2}}\cdot\dfrac{6}{\dfrac{3}{2}}\\\\xy=3\cdot\dfrac{2}{3}\cdot6\cdot\dfrac{3}{2}\\\\xy=18$

Answer 2

Answer:

The product of x and y is 8.

Step-by-step explanation:

It is given that

$x=\log_{5\sqrt{5}}\left(125\right)$

$y=\log_{2\sqrt{2}}\left(64\right)$

We need to find the product of x and y.

$x\cdot y=\log_{5\sqrt{5}}\left(125\right)\cdot\log_{2\sqrt{2}}\left(64\right)$

It can be written as

$xy=\log_{5\sqrt{5}}\left(5\sqrt{5}\right)^2\cdot\log_{2\sqrt{2}}\left(2\sqrt{2}\right)^4$

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.