How do you solve #3·8^(2x-5) = 2·3^(-x+5)#?

1 Answer
bp
Dec 1, 2015

#x= 4 + (40ln2)/(ln3-6ln2)#

Explanation:

The given equation can be written as #3. 2^(6x-15) =2.3^(-x+5)#
Or, #2^(6x-16) = 3^(-x+4)# on dividing both sides by 6.

Now taking natural log on both sides, it would be#(6x-16) ln 2= (-x+4)ln3#

#(6x-16)/(-x+4)= ln3 /ln2#, Or, # -40/(-x+4)= ln3/ln2 -6= (ln3-6ln2)/ln2#

#-x+4= (-40ln2)/(ln3-6ln2)#

#x= 4 + (40ln2)/(ln3-6ln2)#

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