How do you solve #2^x = 5^(x - 2) #?

1 Answer
Shwetank Mauria
Mar 4, 2016

#x=3.513#

Explanation:

To solve #2^x=5^(x−2)#, take logs of both the sides, this becomes

#xlog2=(x-2)log5=xlog5-2log5# and transposing terms this becomes

#xlog5-xlog2=2log5# or

#x(log5-log2)=2log5#

#x=(2log5)/(log5-log2)=(2xx0.699)/(0.699-0.301)# or

#x=1.398/0.398=3.513#

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