etudiante9c2

2022-04-24

how to find the value of $\mathrm{log}}_{37$

silviavalls1005r

Beginner2022-04-25Added 11 answers

If you mean, "How can I calculate $\mathrm{log}}_{37$ using the change of base formula?":

I've never memorized the change of base formula, I always re-derive it as needed. The key is to remember what the expression means:${\mathrm{log}}_{3}7=r$ means that ${3}^{r}=7$ . Taking logarithms base b on both sides, we have

${3}^{r}=7$

${\mathrm{log}}_{b}\left({3}^{r}\right)={\mathrm{log}}_{b}\left(7\right)$

$r{\mathrm{log}}_{b}3={\mathrm{log}}_{b}7$

$r=\frac{{\mathrm{log}}_{b}7}{{\mathrm{log}}_{b}3}$

$\mathrm{log}}_{3}7=\frac{{\mathrm{log}}_{b}7}{{\mathrm{log}}_{b}3$

So if you want to compute$\mathrm{log}}_{37$ using the natural log, you would have

$\mathrm{log}}_{3}7=\frac{\mathrm{ln}7}{\mathrm{ln}3$

If you want to compute them using the common logarithm (base 10), you would compute

${\mathrm{log}}_{3}7=\frac{\mathrm{log}7}{\mathrm{log}3}.$

I've never memorized the change of base formula, I always re-derive it as needed. The key is to remember what the expression means:

So if you want to compute

If you want to compute them using the common logarithm (base 10), you would compute

$\frac{20b}{{\left(4{b}^{3}\right)}^{3}}$

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