Question

Rewrite the logarithm in terms of variables given

Log_9 (12) =a

Log_9 (5) =b

Log_9 (8)=c

Rewrite: Log_9 (1/192)

Answer 1

\[192 = 12 \times 8 \times 8^{1/3} \]

Answer 2

\[ \log_9 \left(1/192\right)=-\log_9 (192) = -\log_9(12\times 8 \times 8^{1/3}) = \cdots\]

Answer 3

-A-B-(b/3)?

Answer 4

Yup :)

Answer 5

Oh so we do not include log _9 (1)?

Answer 6

\[\log(1/k) \\= \log(1) - \log(k)\\ = 0 - \log(k) \\= -\log(k)\]

Answer 7

or\[\log(1/k) \\ = \log(k^{-1}) \\ = - 1\cdot \log(k) \\ = -\log(k)\]

Answer 8

Hogg. And also, how did you know to use 8^(1/3)?

Answer 9

Experience, do enough of these and you see the tricks

Answer 10

My brain wouldn't have thought about that. So would there be a way to figure it out

Answer 11

Ok.

Answer 12

I tried to express 192 as a product of powers of 12, 8 and 5.

There can't be a 5 in there, so that is ruled out.\[12 \times 8 = 96\]I just need to multiply that by 2. I don't have 2 explicitly, but I can write that as the cube root of 8.

Answer 13

Thank you. I couldn't figure out what to do with the last 2 XD