SOLUTION: Prove the product property of logarithms, log_b mn = log_b m+ log_b n, using the properties of exponents. The work is started for you. Let w=log_b m and v=log_b n

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Prove the product property of logarithms, log_b mn = log_b m+ log_b n, using the properties of exponents. The work is started for you. Let w=log_b m and v=log_b n      Log On


   

Question 1127320: Prove the product property of logarithms, log_b mn = log_b m+ log_b n, using the properties of exponents. The work is started for you.
Let w=log_b m and v=log_b n
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


Log base b of n is the exponent to which b must be raised to give you n.

+mn+=++b%5E%28%28log%28b%2C%28m%29%29%29%29%2A+b%5E%28%28log%28b%2C%28n%29%29%29%29+


Using +x%5E%28a%29+%2A+x%5E%28b%29+=+x%5E%28a%2Bb%29+ :

+mn+=+b%5E%28%28log%28b%2C+%28m%29%29+%2B+log%28b%2C%28n%29+%29+%29%29+

Taking log_b of both sides:
+log%28b%2C%28mn%29%29+=+log%28b%2C+%28m%29%29+%2B+log%28b%2C%28n%29+%29++