Arithmetic with the natural log

Question

We have:

$$ \ln(p^3 + 4) - \ln(4) = 2$$

What I did is:

$$ \ln (p^3 + 4) = \ln(4) + \ln(e^2)$$

$$p^3 + 4 = 4 + e^2$$

$$ p = e^{2/3}$$

Why is this incorrect?

The mistake is in going from $\log4+\log e^2$ to $4+e^2$. – Gerry Myerson Jun 01 '13 at 12:40 — Gerry Myerson, Jun 01 '13 at 12:40

score 3 · Accepted Answer · answered Jun 01 '13 at 12:43

3

Correct your mistake using this equality $$\log (a)+\log(b)=\log(ab)$$

answered Jun 01 '13 at 12:43

score 0 · Answer 2 · answered Jun 01 '13 at 12:55

0

$$\log(p^3+4)-\log 4=2\iff \log\frac{p^3-4}4=2\iff \frac{p^3-4}4=e^2\ldots\ldots$$

answered Jun 01 '13 at 12:55

DonAntonio

2 Answers2