How do you solve #log(5-2x)=log(3x +1)#?

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Answer 1 · 2015-08-09T23:51:48

#color(red)(x=4/5)#

#log(5−2x)=log(3x+1)#

Convert the logarithmic equation to an exponential equation.

#10^(log(5-2x)) = 10^(log(3x+1))#

Remember that #10^logx =x#, so

#5-2x=3x+1#

#4=5x#

#x=4/5#

Check:

#log(5−2x)=log(3x+1)#

If #x=4/5#,

#log(5−2(4/5))=log(3(4/5)+1)#

#log(5-8/5)=log(12/5+1)#

#log((25-8)/5)= log((12+5)/5)#

#log(17/5) = log(17/5)#

#x=4/5# is a solution.