How do you solve #2^x = 5^(x+6)#?

1 Answer
Özgür Özer
Dec 2, 2015

#6log_(2/5)5#

Explanation:

#2^x=5^(x+6)#
#=>log_5 2^x=x+6# (logarithm definition)
#xlog_5 2=x+6# (the logarithm of the power of a number)
Divide both sides into #x#:
#=>1/x*(xlog_5 2)=1/x*(x+6)#
#=>(x+6)/x=log_5 2#
Add #-1# to both sides:
#(x+6)/x-1=log_5 2-1#
#=>6/x=log_5 2-1#
#=>x=6/(log_5 2-1)#
#=6/(log_5 2-log_5 5)#
#=6/log_5 (2/5)#
#=6log_(2/5)5#

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