Question

log (a-9) + log a =1 then find the value of "a"

Answer 1

it is the answer of the question

Answer 2

The value of a is  - 1, 10.

Given: log ( a - 9 ) + log a = 1

To Find: The value of a.

Solution:

We know that by the properties of the log, we can say that;

• log a ( MN ) = log a M + log a N
• log a ( M/N ) = log a M - log a N
• log a M = k

       ⇒ M = a^k

Where M, N, and k are positive constants.

Coming to the numerical, we are given,

       log ( a - 9 ) + log a = 1

From the first property, we can say that;

   ⇒  log [ a × ( a - 9 ) ] = 1

Since the base is not given, we can assume it to be 10 by default;

   ⇒  a × ( a - 9 ) = 10^1

   ⇒  a² - 9a - 10 = 0

   ⇒  a² - 10a + a - 10 = 0

   ⇒  a ( a - 10 ) + 1 ( a - 10 ) = 0

   ⇒  ( a - 10 ) ( a + 1 ) = 0

   ⇒   a = - 1, 10

Hence, the value of a is  - 1, 10.

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