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ASHA 777 [7]
3 years ago
8

HELP ASAP!!!!! Pre-calculus

Mathematics
2 answers:
NeX [460]3 years ago
8 0

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

elena-14-01-66 [18.8K]3 years ago
3 0

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.

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