How do you solve #log( - 2a + 9) = log ( 7- 4a )#?

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Answer 1 · 2017-12-06T02:13:46

#a=-1#

First, get rid of #log# by doing the opposite, which is taking each side as an exponent of #10#.

#10^(log(-2a+9))= 10^(log(7-4a))#

this gets you to
#-2a +9 = 7-4a#

Bring all the unknowns to one side by adding #4a# to both sides or by adding #2a# to both sides

#2a + 9 = 7# or #9=7-2a#

subtract either #9# or #7# from both sides so the unknown is by itself.

#2a=-2# or #2=-2a#

divide #2a# by #-2# or #-2a# by #2#

the answer is that #a=-1#