SOLUTION: If log5√5^125=x and log2√2^64=y, the product of x and y is

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Question 1168855: If log5√5^125=x and log2√2^64=y, the product of x and y is
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
see my worksheet below:



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 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 tutorial on properties of logs can be found at http://home.windstream.net/okrebs/page56.html

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

theo