Multiplication of logarithms

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'.

Examples:

    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 (y^x)



    Q) Multiply log (a) with log (b)

    A)    log (a) * log (b) = log (b^log(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)}

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Logarithm of Zero