Question

how to simplify this log stuff?

Answer 1

\[\log_{1/4} (\sqrt[3]{32})\]

Answer 2

first can u write \(\sqrt[3]{32} \) as \((2^5)^{1/3}\)??

Answer 3

yes and?

Answer 4

use the property \(log a^n=nlog a\)

Answer 5

so u get
\((5/3)log_{1/4}2\)
got this ?

Answer 6

i have to simplify to an exact number

Answer 7

oh, that was just intermediate step, its not finished yet, i was just asking whether u understood how i got that.....

Answer 8

then use the log property that:
\(\large log_ab=\frac{log b}{log a}\)

Answer 9

so u get
\((5/3)\frac{log 2 }{log 1/4}\)
and since \(1/4 = 2^{-2}\)
\(\huge(5/3)\frac{log 2 }{log 2^{-2}}\)
can u simplify the denominator now ?

Answer 10

wow u are really a super saiyan

Answer 11

u got the answer ?

Answer 12

ye thx