Question

log x+log(x-4)=log 21

Answer 1

log x + log (x-4) - log 21 = 0

using logarithmic properties...

\(\huge \log \frac{x(x-4)}{21} = 0\)

what do you think comes next?

Hint: if you see no base in log that automatically means the base is 10 :D

Answer 2

it has a base of A

Answer 3

oh..there's a given base?

Answer 4

y

Answer 5

what? it has a base of "y"? please be clear...

Answer 6

i must solve for x

Answer 7

i meant yes

Answer 8

ahh the base matters not :D the next step is to actually change the logarithm to exponential..so even if it's A...

\(\huge A^0 = \frac {x(x-4)}{21}\)

\(\huge 1 = \frac{x(x-4)}{21}\) \(\huge \leftarrow\) see? it will still come out as one

now...what do you think is the next step?

Answer 9

log 1=0 but log 1 with a base of a not = 0

Answer 10

hmmm not quite..i think we're finished with logs..let's not make it complicated..

what you do here is to cross multiply so you'll have..

21 = x(x-4)

now we distribute the x to the values in the parenthesis..

21 = x(x) - x(4)
21 = x^2 - 4x

can you do the rest?

Hint: transpose; then use factoring/completing the square

Answer 11

if i agree with u it gives 7 ....Am i right?

Answer 12

hmm..7 is ONE of the there's another one...can you find it?.

Answer 13

the other is rejected coz it is negative which is undefined with log

Answer 14

right :D \(\large \checkmark\)

Answer 15

but i m not really sure that log(1) with a base of A gives 0

Answer 16

log 1 base A = 0 it is in one of the logarithmic properties...

see here http://www.zweigmedia.com/RealWorld/calctopic1/logs.html

just scroll down you'll see a list of the logarithmic properties

Answer 17

u r right sorry for ur time and thks a lot for ur help

Answer 18

<tips hat>

Answer 19

the answer is 7.am i right?