Question

Log^6 432 - log^6 12

Answer 1

Ответ:

2.

Пошаговое объяснение:

log(6) 432 - log(6) 12 = log(6) (432:12) = log(6) 36 =log(6) 6^2 = 2• log(6) 6 = 2•1 = 2

Answer 2

To simplify the expression $\log^6 432 - \log^6 12$, you can use logarithmic properties, especially the subtraction rule:

$\log_a (b) - \log_a (c) = \log_a \left(\frac{b}{c}\right)$

In your case, $a = 6$, $b = 432$, and $c = 12$. Applying the subtraction rule:

$\log^6 432 - \log^6 12 = \log^6 \left(\frac{432}{12}\right)$

Now, simplify the fraction:

$\log^6 \left(\frac{432}{12}\right) = \log^6 (36)$

Next, use the fact that $36 = 6^2$:

$\log^6 (6^2)$

Now, you can see that $\log^6 6^2$ can be simplified by taking the 6th root of $6^2$ because the logarithm and the power cancel out:

$6^{\frac{2}{6}}$

Now, simplify the exponent:

$6^{\frac{1}{3}}$

So, the final simplified expression is $6^{1/3}$.