Question

If log (a+b)=log a +log b find a in terms of b

Answer 1

log(a+b)=log a + log b
log(a+b)=log ab according to logarithm log m + log n = logmn
log gets cancelled
a+b=ab
b=ab-a
b=a(b-1)
b/a=b-1
b/a+1=b
b+a/a=b

Answer 2

Hence, a = b/(b - 1).

Given:

log (a + b)=log a +log b

To Find:

The value of 'a' in terms of 'b'.

Solution:

We have been given that

log (a + b) = log a +log b       ...................................(I)

To solve this problem, we will be applying the product rule of logarithms, which states that the logarithm of a product is equal to a sum of logarithms.

Hence if 'a' and 'b' are two numbers, then

log(ab) = log a +log b           ...................................(II)

From equations (I) and (II) we have

log (a + b) = log(ab)

by taking antilog on both sides

⇒ a + b = ab  .........................   (by taking antilog on both sides)

Dividing both sides by a, we get

1 + b/a = b

⇒ b/a = b - 1

⇒ a = b/(b - 1)

Hence, a = b/(b - 1).

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