Question

write 1-3log5x as a single logarithm

Answer 1

\[1 - 3\log _{5}x\]

Answer 2

@jim_thompson5910

Answer 3

how far did you get

Answer 4

nowhere.

Answer 5

i don't know what a single logarithm looks like

Answer 6

it looks like log(...) where the log is any base and there are no terms outside the log

Answer 7

okay i know what you mean now

Answer 8

try to get the given expression into the form I wrote

Answer 9

i don't know how to go about doing that

Answer 10

if someone could actually help me that would be great.

Answer 11

hints:

\[\large \log_{b}(b) = 1\]

\[\large y\log_{b}(x) = \log_{b}(x^y)\]

\[\large \log_{b}(x) - \log_{b}(y) = \log_{b}\left(\frac{x}{y}\right)\]

Answer 12

okay i see your formulas but i have absolutely no idea what numbers are equivalent to what letters therefore i can't plug anything into a formula.

Answer 13

you can replace b with 5 to go from

\[\large \log_{b}(b) = 1\]

to

\[\large \log_{5}(5) = 1\]

Answer 14

okay i see that.

Answer 15

then what.

Answer 16

use the other formulas I gave you

Answer 17

what is y

Answer 18

compare

\[\large y\log_{b}(x) \]

to

\[\large 3\log_{5}(x)\]

Answer 19

\[3\log _{5}(x) = \log _{5}(x ^{3})\]

Answer 20

good

Answer 21

we have this so far


\[\large 1 - 3\log_{5}(x)\]


\[\large \log_{5}(5) - 3\log_{5}(x)\]


\[\large \log_{5}(5) - \log_{5}(x^3)\]

Answer 22

\[\log _{5}(x) - \log _{5}(3) = \log _{5}(\frac{ x }{ 3 })\]

Answer 23

not quite

Answer 24

\[\large \log_{5}(5) - \log_{5}(x^3)\]

turns into this

\[\large \log_{5}\left(\frac{5}{x^3}\right) \]

(see rule #3 given above)

Answer 25

so this is the complete step by step picture

Answer 26

\[\large 1 - 3\log_{5}(x)\]


\[\large \log_{5}(5) - 3\log_{5}(x)\]


\[\large \log_{5}(5) - \log_{5}(x^3)\]


\[\large \log_{5}\left(\frac{5}{x^3}\right) \]

Answer 27

and that's your answer huh

Answer 28

yes

Answer 29

thank you a ton for your patience

Answer 30

sure thing