1. Given the product law of logarithms, prove the product law of exponents.

2. Given the quotient law of logarithms, prove the quotient law of exponents.

3. Apply algebraic reasoning to show that

a=b^(loga/logb) for any a,b>0

Please explain these to me.

All I know is that

The product law of logs are:

Log(AB)=logA+logB

The Quotient law of logs are:

Log(A/B)=logA-Logb

Edit:

For product law:

let m=b^x and let n=b^y

mn=(b^x )(b^y)

and then what should i do?