How do you solve for x and y if log x - log y =2 and log x + log y = 0?

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Answer 1 · 2016-09-01T23:00:20

The point of intersection is #(10, 1/10)#, assuming the logarithms are in base #10#.

Isolate the #logx# in equation #1#.

#logx = 2 + logy#

Substitute for #logx# in equation #2#:

#2 + logy + logy = 0#

#2 + 2logy = 0#

#2(1 + logy) = 0#

#logy = -1#

#y = 10^-1#

#y = 1/10#

#:.logx = 2 + log(1/10)#

#logx - log(1/10) = 2#

#log(x/(1/10)) = 2#

#10x = 10^2#

#10x = 100#

#x = 10#

The solution point is #(10, 1/10)#.

Hopefully this helps!