Question 632898: find the value of 0.356*200*4*0.7using logarithms?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! equation is:
y = 0.356*200*4*0.7
take log of both sides of the equation to get:
log(y) = log(0.356*200*4*0.7)
since log(a*b) = log(a) + log(b), this equation now becomes:
log(y) = log(0.356) + log(200) + log(4) + log(0.7)
use your calculator to find the logs of all the terms on the right side of the equation to get:
log(y) = -.448550002 + 2.301029996 + .6020599913 - .15490196
combine like terms to get:
log(y) = 2.299638025
since log(y) = x if and only if 10^x = y, than this equation becomes:
y = 10^2.299638025
use your calculator to get y = 199.36
you can confirm this is true by using your calculator to solve for y in the original equation of y = 0.356*200*4*0.7
you get y = 199.36
since this is the same answer you got using logarithms, you can be confident that you calculated through logarithms correctly.
note that:
log(x) is the same as log(10,x) which means log of x to the base of 10.
not that log(y) = x if and only if 10^x = y
not also that log(x) = y if and only if 10^y = x
note also that, in the equation above of y = 10^2.299638025, x was assumed equal to 2.299638025.
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