I don't know how they're the same, would someone please help and please show all of your working out. Thank you in advance.
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log[(x + 2)(x - 3)]
First, let x + 2 = a and x - 3 = b.
log(ab)
But a = 10^(loga) and b = 10^(logb)
= log[10^loga*10^logb]
By exponent laws:
= log[10^(loga + logb)]
And since log and 10^ are inverse functions:
= loga + logb
So:
= log(x + 2) + log(x - 3)
First, let x + 2 = a and x - 3 = b.
log(ab)
But a = 10^(loga) and b = 10^(logb)
= log[10^loga*10^logb]
By exponent laws:
= log[10^(loga + logb)]
And since log and 10^ are inverse functions:
= loga + logb
So:
= log(x + 2) + log(x - 3)