Question

Hello! I have a problem with logarithms again :/ Can anyone help me? If \[\log _{a}\sqrt[5]{16}=-1.6\] then a is:

A 0.5\[B \sqrt{2}\]\[C -\frac{ \sqrt{2} }{2 }\] \[D \frac{ \sqrt{2} }{2 }\]

Well, i think I should to like this:
\[a ^{-1.6}=16^{\frac{ 1 }{ 5 }}\]

But what is next?

Answer 1

can you help me, @RadEn

Answer 2

-1.6 = -16/10 = - 8/5
do u agree with that ^ ?

Answer 3

yes, of course.

Answer 4

also, (16)^(1/5) = (2^4)^(1/5) = 2^(4/5)

Answer 5

yup

Answer 6

So now I have:

\[a ^{-\frac{ 8 }{ 5 }}=2^{\frac{ 4 }{ 5 }}\]
right?

Answer 7

sorry, my conection is lagging :(
yes... that's right
now, use manipulating algebra w'll get :

Answer 8

Sorrry, @RadEn , I cant see your message://

Answer 9

\[log_a16^{1/5}=-1.6\]\[1/5\ log_a16=-1.6\]\[log_a16=-8.0\]Identify\[log_ax=y,\ a^y=x\]\[x=16,\ y=-8\]\[a^{-8}=16\]\[a^8=16^-\]\[a=(1/2^4)^{1/8}\]\[a=2^{-1/2}\]\[a=1/\sqrt2=\sqrt{2}/2\]

Answer 10

yeah, my conection very-very slow :(

Answer 11

If we need to go over any steps post which line

Answer 12

Omg! It was easy ;/ Thank you a lot, stamp and Rad!