Log(x+4)-log(x-2)=1
step by step please!

x

=

7

9

.

Step-by-step explanation:

x

=

7

9

.

Explanation:

Remember the rules of logarithms:

log

a

−

log

b

=

log

(

a

b

)

. Using this, we get

log

x

−

log

(

x

+

7

)

=

−

1

⇒

log

(

x

x

+

7

)

=

−

1

Now we remember that

log

c

=

d

⇔

c

=

10

d

. Essentially what we're doing there is taking 10 to the power of both sides, and since

10

x

and

log

x

are inverse functions, they cancel off.

f

−

1

[

f

(

x

)

]

=

x

. So we get

log

(

x

x

+

7

)

=

−

1

(

⇒

10

log

(

x

x

+

7

)

=

10

−

1

)

⇒

x

x

+

7

=

10

−

1

⇒

x

=

x

+

7

10

⇒

10

x

=

x

+

7

⇒

9

x

=

7

⇒

x

=

7

9

So

x

=

7

/

9

is our answer.