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

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Answer 1 · 2015-08-01T19:14:26

#color(red)(x=16)#

#log(x+9) = log (2x-7)#

Convert the logarithmic equation to an exponential equation.

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

Remember that #10^logx =x#, so

#x+9 = 2x-7#

Move all terms to the right hand side.

#0 =2x-7-x-9#

Combine like terms.

#0 =x-16#

#x=16#

Check:

#log(x+9) = log (2x-7)#

If #x=16#

#log(16+9) = log (2(16)-7)#

#log25 = log (32-7)#

#log25 = log25#

#x=16# is a solution.