Solve for $x$ and $y$ for which $(0.2)^{x}(0.5)^{y} = 200$.
Solution
$(0.2)^{x}(0.5)^{y} = 200$
$\left(\frac{2}{10} \right)^{x} \left(\frac{5}{10} \right)^{y} = (2^{3})(5^{2})$
$\left(\frac{1}{5} \right)^{x} \left(\frac{1}{2} \right)^{y} = (2^{3})(5^{2})$
$(5^{-x})(2^{-y}) = (2^{3})(5^{2})$
$(5)^{-x}(2)^{-y} = (5^{2}) (2^{3})$
Comparing powers of like terms for both sides:
$-x = 2$
$x = -2;$
$-y = 3$
$y = -3.$
Therefore $x = -2 \ \text{and} \ y = -3$.
Any Alternative approach?
-
- Active Topics
-
-
- by Eli 10 hours ago Re: What is in Your Mind? View the latest post Replies 689 Views 274146
- by Eli 2 days ago Iran Launches Retaliatory Attack Against Israel, and Israel Retaliates by Attacking Iranian Isfahan Millitary Base View the latest post Replies 28 Views 890
- by Eli 3 days ago All in One: YouTube, TED, X, Facebook and Instagram Reels, Videos, Images and Text Posts View the latest post Replies 319 Views 9008
- by Eli 6 days ago Python Packages for Scientific Computing View the latest post Replies 8 Views 3011
- by Eli 6 days ago Dunia Yetu: Building Tanzania's Digital Future Together View the latest post Replies 5 Views 1845
- by Eli 1 week ago Russia Invades Ukraine View the latest post Replies 646 Views 210474
- by Eli 1 week ago Programmatically Move Files from One Folder to Another View the latest post Replies 6 Views 1431
- by Eli 2 weeks ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 33 Views 43755
- by Eli 2 weeks ago What is Retrieval-Augmented Generation (RAG)? View the latest post Replies 2 Views 361
- by Eli 2 weeks ago Chat With ChatGPT - An Interactive Conversational AI View the latest post Replies 22 Views 24377
-
Solving for unknowns
-
- Information
-
Who is online
Users browsing this forum: No registered users and 0 guests