Question

prove that a^log m+log n=mn​

Answer 1

Answer:

Let m = logₐ M and n = logₐ N, so, by definition, M = a^m and N = aⁿ. Then:

MN = a^m × aⁿ = a^(m + n )

- where we have used the appropriate rule for exponents. From this, using the definition of a logarithm, we have:

m + n = logₐ (MN)

But m + n = logₐ M + logₐ N, and the above equation may be written:

logₐ M + logₐN = logₐ (MN)

Proved

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Step-by-step explanation: