Question

which one is the same as log(3x) 5y ?
a. log 5x/3y
b. log 3x/5y
c. log(5y)/log(3x)
d. log(3x)/log(5y)
3x is the base, by the way.

Answer 1

Are you familiar with the change of base rule?

Answer 2

If not, the change of base rule says

\[\Large \log_{b}(x) = \frac{\log(x)}{\log(b)}\]

Answer 3

not really :/

Answer 4

What is the base in your problem?

Answer 5

3x

Answer 6

good, so b = 3x

Answer 7

so logx/log3x?

Answer 8

The argument (the stuff inside the log) is 5y, so we replace that 'x' in the formula I wrote above with '5y' to get...


\[\Large \log_{3x}(5y) = \frac{\log(5y)}{\log(3x)}\]

Answer 9

ohhh. okay! so is that how it always is on these types of problems?

Answer 10

yes

Answer 11

okay (: thank you!

Answer 12

any time you have a log and you want to write in another base, then you'll use the change of base formula

Answer 13

you're welcome

Answer 14

i have one more question :P


what is the solution to log3x-2 125 = 3 ?

3x-2 is the base

Answer 15

\[\Large \log_{3x-2}(125) = 3\]


\[\Large (3x-2)^3 = 125\]


\[\Large 3x-2 = \sqrt[3]{125}\]


\[\Large 3x-2 = 5\]


I'll let you finish

Answer 16

so its... 3x =
x = 3/3
which x=1 ?

Answer 17

no, you add 2 to both sides to get


\[\Large 3x-2 = 5\]

\[\Large 3x-2+2 = 5+2\]

\[\Large 3x = 7\]

Answer 18

ADD two . shoot i subtracted . my bad . so 7/3 is the answer then !

Answer 19

you nailed it

Answer 20

thank yo uso much :D

Answer 21

sure thing