Law of multiplication of logarithms:Any quantity that is multiplied with a logarithm goes to the exponent of the logarithm's number.
n * log (a) = log (an)Here 'n' is any value being multiplied with the logarithm. After multiplication, the value 'n' become the exponent of the logarithm's number 'a'.
Q) Multiply 2 with log(4)
A) 2 log (4) = log (42)
= log (16)
Q) Multiply x with log(y)
A) x * log (y) = log (yx)
Q) Multiply log (a) with log (b)
A) log (a) * log (b) = log (blog(a))
Q) Multiply 2 with log (x + y)
A) 2 * log (x + y) = log (x + y)2
= log (x2 = y2 = 2xy)
Q) Multiply (x + y) with log (x + y)
A) (x + y) * log (x + y) = log (x + y)(x + y)