Question

if log (a+1) = log (4a-3) - log 3; find a

Answer 1

log(a+1) = log(4a-3) - log 3
log(a+1) = log (4a-3/3)
a+1 = 4a-3/3
3(a+1) = 4a -3
3a + 3 = 4a - 3
3a - 4a = -3 -3
-a = -6
a = 6

Answer 2

The value of a is "6".

Explanation:

We have,

$\log (a+1)=\log (4a-3)-\log 3$

⇒ $\log (a+1) + \log 3=\log (4a-3)$

⇒ $\log (\dfrac{a+1}{3} )=\log (4a-3)$

[∵ $\log m + \log n=\log mn$ }

⇒$3a+3 = 4a-3$

⇒ a = 6

Hence, the value of a is "6".