Question 1168855
see my worksheet below:


<img src = "http://theo.x10hosting.com/2020/110302.jpg" >


your solution is that the product of x and y is 2000.


the solution depends on the following concepts.


sqrt(x) = x^(1/2)


log(a^x) = x * log(a)


(x^a)^b = x^(a * b)


logb(x) = log(x)/log(b)


log(b)/log(b) = 1


to be more specific:


the following things were done to log5(sqrt(5^125))


sqrt(5^125) was converted to (5^125)^(1/2)


(5^125)^(1/2) was converted to 5^(125 * 1/2) = 5^62.5


log5(5^62.5) was converted to 62.5 * log5(5)


log5(5) was converted to log(5)/log(5)


the same things were done to log2(sqrt(2^64))


a tutorial on log base conversion can be found at <a href = "http://home.windstream.net/okrebs/page57.html#:~:text=Change%20of%20base%20formula%20Log,base%20in%20the%20new%20base.&text=Solution%3A%20Change%20to%20base%2010%20and%20use%20your%20calculator.&text=Now%20use%20your%20calculator%20and%20round%20to%20hundredths." target = "_blank">http://home.windstream.net/okrebs/page57.html#:~:text=Change%20of%20base%20formula%20Log,base%20in%20the%20new%20base.&text=Solution%3A%20Change%20to%20base%2010%20and%20use%20your%20calculator.&text=Now%20use%20your%20calculator%20and%20round%20to%20hundredths.</a>


a tutorial on properties of logs can be found at <a href = "http://home.windstream.net/okrebs/page56.html" target = "_blank">http://home.windstream.net/okrebs/page56.html</a>


i'll be available to answer any questions you might have about this.


theo