How do you expand $ln (\frac{x}{\sqrt{x^{6} + 3}})$ $ln(x/sqrt(x^6+3))$ ?

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Answer 1 · 2016-09-04T22:25:22

The expression can be simplified to $ln x - \frac{1}{2} ln (x^{6} + 3)$ $lnx - 1/2ln(x^6 + 3)$

Start by applying the rule ${log}_{a} (\frac{n}{m}) = {log}_{a} (n) - {log}_{a} (m)$ $log_a(n/m) = log_a(n) - log_a(m)$ .

$\Rightarrow ln (x) - ln (\sqrt{x^{6} + 3})$ $=>ln(x) - ln(sqrt(x^6 + 3))$

Write the $\sqrt$ $√$ in exponential form.

$\Rightarrow ln x - {ln (x^{6} + 3)}^{\frac{1}{2}}$ $=> lnx - ln(x^6 + 3)^(1/2)$

Now, use the rule $log (a^{n}) = n log a$ $log(a^n) = nloga$ .

$\Rightarrow ln x - \frac{1}{2} ln (x^{6} + 3)$ $=>lnx - 1/2ln(x^6 + 3)$

This is as far as we can go.

Hopefully this helps!

How do you expand ln(x/sqrt(x^6+3))ln(x√x6+3)ln(x/sqrt(x^6+3))?