Question

HOW WE SOLVE THIS \[log_{2}(x+3)+log_{3}(x+2)=1\]

Answer 1

I know the answer is -1

Answer 2

I am sure @bhaskarbabu will do this..

Answer 3

ya its -1
its little bit lengthy to explain just wait for a while

Answer 4

loga + logb = logab
First use this...

Answer 5

\[\log_{y} x = \ln x /\]
Then use this

Answer 6

ln y

Answer 7

So, we get (x+3)(x+2) = 2
You get a quadratic equation...Solve

Answer 8

can't do that. tthe base for 2nd is 3

Answer 9

You get -1 and -4

Answer 10

But -4 is not valid as it does not follow rules of log

Answer 11

Oh sorry..I saw it as 3..

Answer 12

log(x+3)
2
= log3
3
- log(x+2)
3
log(x+3)
2
= log(3/x+2)
3
ln(x+3)
ln2
=ln(3/x+2)
ln3
ln3 * ln(x+3) = ln(2)
* ln(3/x+2)
hence x+3=2 and 3/x+2
=3

Answer 13

hence x=-1

Answer 14

can't understand that :(

Answer 15

\(log_2 (x+3) = log_3 3 - log_3(x+2) \\ log_2 (x+3) = log_3 (3/x+2)\)

Answer 16

till here, i understood ur work @bhaskarbabu

Answer 17

He equaled the variable terms on side to the constant terms on the other side...Its a good way actually..

Answer 18

@ganeshie8 after that he made all the bases to e..that is he changed them into natural logarithms..

Answer 19

next u converted everything to natural log, but hw u conclude x from there ?

Answer 20

now cross multiply

Answer 21

\[\log_{y} x = \ln x / \ln y\]

Answer 22

@bhaskarbabu I get it.
Excellent work.
wow!!!!!!!

Answer 23

wow !! i see it too :) amazing work !!!!