Question

please show how to write this expression as a single logarithm::::: Give me a second to post the expression

Answer 1

\[-2\log_{3} (1/x)+1/3\log_{3}\sqrt{x} \]

Answer 2

\[\log_b(A) + \log_b(B) = \log_b(AB)\]\[\log_b(A) - \log_b(B) = \log_b \left( \frac{ A }{ B } \right)\]\[\log_b(A^B) = B\ \log_b(A)\]

Answer 3

use the third one first, then the first one

Answer 4

i got \[\log_{3}x^(1/6)\]

Answer 5

-2log(1/x) = log(1/x)^(-2) = log(1/x^(-2)) = log(x^2)

1/3log(sqrt(x)) = 1/3log(x)^(1/2) = log((x)^(1/2))^(1/3) = log(x)^(1/6)

log(x^2) + log(x)^(1/6) = log(x^2 * x^(1/6)) = log(x)^(2+1/6) = log(x)^(13/6)
= 13/6 * log(x)

The log is to the base 3.

Answer 6

thank you : )

Answer 7

you are welcome :)