Log x + log (x + 9) = 1

x = 1

Step-by-step explanation:

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x=1

Step-by-step explanation:

See below

Explanation:

Our goal is to have an expresion like this

log

A

=

log

B

due to one to one aplication of logarithm, we get

A

=

B

. We have to apply the rules of logarithm for product, quotient and power and use the fact

log

10

=

1

log

x

+

log

(

x

+

9

)

=

1

log

x

(

x

+

9

)

=

log

10

Now, we know that

x

(

x

+

9

)

=

10

x

2

+

9

x

−

10

=

0

using quadratic formula we get

x

=

−

10

and

x

=

1

reject negative because there is no logarithm and the only solution is

x

=

1

. Lets check it

log

1

+

log

(

1

+

9

)

=

0

+

1

=

1