Question 20543
Recall:

If log{{{6}}}a = log{{{6}}}b, then a = b

log{{{6}}}(2x-5) = log{{{6}}}(7x+10)
(2x-5) = (7x+10) Subtract 2x from both sides.
-5 = 5x+10 Subtract 10 to bothsides.
-15 = 5x Divide both sides by 5.
x = -3

Check:
log{{{6}}}(2(-3)-5) = log{{{6}}}(7(-3)+10)
log{{{6}}}(-11) = log{{{6}}}(-21+10)
log{{{6}}}(-11) = log{{{6}}}(-11)