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

1 Answer
Nov 4, 2016

Answer:

Set the expressions equal to find #a=-1#

Explanation:

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

If the log of an expression equals the log of another expression, the two expressions must be equal.

#-2a+9=7-4a#
#+4acolor(white)(aaaaa^22a)+4a#

#color(white)(a^2)2a+9=color(white)(aa)7#
#color(white)(aa^2a)-9=-9#

#color(white)(a^2)(2a)/2=(-2)/2#

#color(white)(aaa^2)a=-1#