If log5 x - log5(x - 2) = 3, then the value of x, to the nearest hundredth, is?

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Answer 1 · 2017-01-13T00:21:37

#x ~= 2.02# (Assuming #log5# represents #log_5#)

Assuming #log5# represents #log_5# (log to the base 5), we have:

#log_5x-log_5(x-2)=3#

#log_5(x/(x-2)) =3#

#x/(x-2) = 5^3 = 125#

#x=125(x-2)#

#124x = 250#

#x=250/124 ~= 2.02# (To the nearest hundredth as requested)

However, to perform a check you should use 8 decimal places:
#x~= 2.01612903#