Question

expand the given logarithm and simplify

Answer 1

\[\log_{\sqrt{2}} (4x ^{3})\]

Answer 2

you can break up the product into a sum of logs with the same base sqrt(2)

Answer 3

i just looked at a video on youtube about this can i do it like this
log√2(4x3)= log√2(4)+3log√2(x)

Answer 4

It may be wise to change bases - maybe Base 2

\(\log_{\sqrt{2}}(4x^{3}) = \dfrac{\log_{2}(4x^{3})}{\log_{2}(\sqrt{2})} = \dfrac{2 + 3\log_{2}(x)}{1/2} = 4 + 6\log_{2}(x)\)

Just guessing. Various things mean "simplified" to various people.

Answer 5

3log√2(x)+4 this was supposed to be the answer

Answer 6

yeah you can do it as
\[\log_{\sqrt2}(4)+\log_{\sqrt2}(x^3)\]
\[=\log_{\sqrt2}(4)+3\log_{\sqrt{2}}(x)\]

Answer 7

then compute
\[\log_{\sqrt2}(4)\]

Answer 8

how would i compute that if you could please explain it to me

Answer 9

anytime i have a number before the exponent and another number but after the log with the same log value i can just connect them?

Answer 10

It may be wise to change bases - maybe Base 2.

Answer 11

how can i change the base?

Answer 12

I GOOTTTTTTTTT ITTTTTTTTTTTTTTTT AAAAAAYYYYYYYYEEEEEE !!!!!! THANKS