How do you solve y = log^3(78.5)?

Feb 8, 2016

$y = 6.80358827392$

Explanation:

There is no way to simplify this, other than writing this as $\log \left(78.5\right)$ multiplied by itself $3$ times.

$y = {\log}^{3} \left(78.5\right) = \log \left(78.5\right) \times \log \left(78.5\right) \times \log \left(78.5\right)$

Note that this is different than the other logarithm rules:

• $\log \left({a}^{b}\right) = b \times \log \left(a\right)$

$\text{ }$This would apply if the question were $\log \left({78.5}^{3}\right)$.

• $\log \left(a\right) + \log \left(b\right) = \log \left(a b\right)$

$\text{ }$This would apply if the question were $\log \left(78.5\right) + \log \left(78.5\right) + \log \left(78.5\right)$.

However, the only way to find this is the use a calculator:

y=log(78.5)xxlog(78.5)xxlog(78.5)=color(blue)(6.80358827392