Question

Solve: log(3) ^(x+4) - log(3) ^x =2

Answer 1

use the log property
\(\Large \log A -\log B = \log (A/B)\)

Answer 2

is it
\(\Large \log 3^{x+4}\)
or
\(\Large \log_3 (x+4)\)

Answer 3

\[ \log(3) ^{(x+4)} - \log(3) ^x =2\]\[(x+4) \log(3) - (x)\log(3) =2\]\[4\log(3) =2\]

So I would therefore sy it is the second thing hartnn posted.

Answer 4

\[\log_3x+4-\log_3x=2\] like tus right ?

Answer 5

yup, that makes more sense

Answer 6

Yes, it is log(3) x+4, sorry it's to differentiate on my paper

Answer 7

ok, use this property for left side
\(\Large \log A -\log B = \log (A/B)\)
what do u get ?

Answer 8

log(3) (x+4)/x

Answer 9

correct!

Answer 10

\(\log_3 [(x+4)/x] = 2\)

now use the definition
\(\Large \log _AB=C \implies B=A^C\)

Answer 11

I'm not sure I'm following that one

Answer 12

Like, 3^2= (x+4)/x?

Answer 13

yeah, thats correct! :)
good.

Answer 14

Then solve for x?

Answer 15

now can you solve further ?
3^2 = 9
then multiply both sides by x

Answer 16

9x=x+4
8x=4
x=2

It's saying the correct answer is 1/2

Answer 17

\[\log_3x+4-\log_3x= 2\]\[\log_3x+4-\log_3x=2~ \log_33\]\[\log_3x+4-\log_3x=\log_33^{2}\]\[\log_3x+4-\log_3x=\log_39\]\[\log_3x+4=\log_39+\log_3x\]\[\log_3x+4=\log_39x\]\[x+4=9x\]\[4=8x\]\[x=1/2\]

Answer 18

8x=4
not 4x=8

Answer 19

8x = 4 gives
x= 4/8 = 1/2

Answer 20

Oh, I see. Thank you!

Answer 21

thats a nice alternative @WHAT?! , good!

Answer 22

tnx :) I just don't like fractions inside the logs.