# Algebra

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Please show me step by step on solving this problem? log₅(2x-9)+ log₅(x+2)= 1
Thank you

I'm getting 2x²-5x-28=0 which is a empty set. Trying to make sure I'm correct if I am. Thanks so much for your help

• Algebra -

log5 [(2x-9)(x+2)] = 1

(2x-9)(x+2) = 5^1 = 5

2 x^2 -5 x -18 = 5

2 x^2 - 5 x - 23 = 0

x = [ 5 +/- sqrt (25+184 ] /4

= [ 5 +/- 14.5 ] /4

= 19.5/4 or -9.46/4

= 4.86 or -2.36

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