Which value of z would satisfy 5z+3 = 5z+2?

Which value of z would satisfy 5z+3 = 5z+2? Correct Answer log (4 / 125) / log (5 / 2)

Given, 5z+3 = 5z+2 ➩ log (5z+3) = log (5z+2) ➩ (z + 3) log 5 = (z + 2) log 2 ➩ z log 5 + 3 log 5 = z log 2 + 2 log 2 ➩ z log 5 – z log 2 = 2 log 2 – 3 log 5 ➩ z = ( 2 log 2 – 3 log 5) / (log5 – log 2) ➩ z = log (22 / 53) / log (5 / 2) ➩ z = log (4 / 125) / log (5 / 2)
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