How do you solve #2 log x = log 25 + 2#?

1 Answer
George C.
Dec 29, 2015

Use the fact that #log(x)# is a one-one function as a Real-valued function of Real numbers to find:

#x = 50#

Explanation:

Divide both sides by #2# to get:

#log(x)#

#= (log(25)+2) / 2#

#= (2 log(5) + 2 log(10))/2#

#= log(5) + log(10)#

#= log(50)#

Hence #x = 50#, since #log(x):(0, oo) -> RR# is one-one.

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