Question

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

Answer 1

Given,

log(a-9)+log a=1

To find,

The value of a

Main solution :

We know that,

log m + log n = log mn

This is called product law.

Using this law,

log (a-9)(a)=1

log a^2-9a=1

We know,

1 = log 10

Substituting this value of 1 in above equation:-

log a^2-9a=log 10

Cancelling logs from LHS and RHS, we get :-

${a}^{2}- 9a=10$

${a}^{2}- 9a-10 = 0$

${a}^{2}+ a - 10a - 10 = 0$

$a(a + 1)- 10(a + 1) = 0$

$(a + 1)(a - 10) = 0$

Now , a = -1 or 10

The base of a logarithm is a positive no.

So, we will take positive value of a.

a=10(Ans)