Question

Simplify:
log2(1024n/log2n)

Answer 1

Not sure what property would help here.

Answer 2

\(\large \mathbb{\frac{\log_2 1024^n}{\log_2 n}}\)

Answer 3

is the question like that ?

Answer 4

the bottom part is

log2(4sqrt(8))

Answer 5

\(\large \mathbb{\frac{\log_2 1024^n}{\log_2 \sqrt{8}}}\)

Answer 6

like that ?
is the top part correct ?

Answer 7

Its log2(1024n/log2n) / log2(4sqrt(8))

the bottom being quad root of 8

Answer 8

\(\bf \large
\cfrac{log_2\left(\frac{1024^n}{log_2n}\right)}{log_2\sqrt[4]{8}}\quad ?\)

Answer 9

Yes, that is correct

Answer 10

execpt it is 1024n, no exponent

Answer 11

ok

Answer 12

http://www.chilimath.com/algebra/advanced/log/images/rules%20of%20exponents.gif <--- notice those rules

\(\bf \large{ {\color{blue}{ 1024\implies 2^{10}\qquad 8\implies 2^3\qquad \sqrt[{\color{red} m}]{a^{\color{blue} n}}=a^{\frac{{\color{blue} n}}{{\color{red} m}}}}} \\ \quad \\ \quad \\

\cfrac{log_2\left(\frac{1024n}{log_2n}\right)}{log_2\sqrt[4]{8}}\implies
\cfrac{log_2\left(\frac{2^{10}n}{log_2n}\right)}{log_2\sqrt[4]{2^3}}\implies \\ \quad \\
\cfrac{log_2\left(\frac{2^{10}n}{log_2n}\right)}{log_2(2^{\frac{3}{8}})}\implies

\cfrac{log_2(2^{10}n)-log_2n}{log_2(2^{\frac{3}{8}})}}\)


see if you can apply the 1st log rule listed on the picture to the numerator

Answer 13

hmmm I have an 8 that came out of nowhere....lemme fix that \(\bf \large{ {\color{blue}{ 1024\implies 2^{10}\qquad 8\implies 2^3\qquad \sqrt[{\color{red} m}]{a^{\color{blue} n}}=a^{\frac{{\color{blue} n}}{{\color{red} m}}}}} \\ \quad \\ \quad \\

\cfrac{log_2\left(\frac{1024n}{log_2n}\right)}{log_2\sqrt[4]{8}}\implies
\cfrac{log_2\left(\frac{2^{10}n}{log_2n}\right)}{log_2\sqrt[4]{2^3}}\implies \\ \quad \\ \quad \\
\cfrac{log_2\left(\frac{2^{10}n}{log_2n}\right)}{log_2(2^{\frac{3}{4}})}\implies

\cfrac{log_2(2^{10}n)-log_2n}{log_2(2^{\frac{3}{4}})}}\)

Answer 14

say what would you get if you were to apply the 1st rule listed at http://www.chilimath.com/algebra/advanced/log/images/rules%20of%20exponents.gif to say \(\bf log_2(2^{10}n)\quad ?\)