Question

Solve exactly for X...
Log(x+3)-log(x+2)=log(4)

Answer 1

well first you do, log((x+3)/(x+2))=log(4) but then what?

Answer 2

raise each side to the power of 10

Answer 3

or equate the arguments

Answer 4

Use the rules of logs:

\(\log a + \log b = \log ab\)

\(\log_b x = y \iff b^y = x\)

If \(\log a = \log b\) then \(a = b\)

Answer 5

\(\log a - \log b = \log \dfrac{a}{b} \)

Answer 6

Correct.

Answer 7

ahhhhh good. i thought so, @mathstudent55
I just wasnt sure..

Answer 8

Look at the third rule above.

Answer 9

\(\log \dfrac{x+3}{x+2} = \log 4\)

Now apply:

\(\log a = \log b\), then \(a = b\)

Answer 10

but my answer comes out to -5/3=x right? doesnt that not work because like -5/3 is less than the base?

Answer 11

or am i just confusing myself?

Answer 12

Once the logs are equal, then

\(\dfrac{x+3}{x+2} = 4\)

Did you solve this equation?

Answer 13

-5/3 ^_^

Answer 14

would that be my final answer?

Answer 15

\(\dfrac{x+3}{x+2} = 4\)

\(x + 3 = 4(x + 2)\)

\(x + 3 = 4x + 8\)

\(3x = -5\)

\(x = - \dfrac{5}{3} \)

Exactly. Good job!

Answer 16

i got one more, you up for helping?

Answer 17

Sure. Pls start a new post.