SOLUTION: Explain the connection between the exponential equation (10^3 x 10^5= 10^8) and the logarithmic equation (log10^3 + log10^5=log10^8)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Explain the connection between the exponential equation (10^3 x 10^5= 10^8) and the logarithmic equation (log10^3 + log10^5=log10^8)      Log On


   

Question 1012074: Explain the connection between the exponential equation (10^3 x 10^5= 10^8) and the logarithmic equation (log10^3 + log10^5=log10^8)
Answer by ValorousDawn(53) About Me  (Show Source):
You can put this solution on YOUR website!
In general log%28ab%29=log%28a%29%2Blog%28b%29 and log%28a%5Eb%29=b%2Alog%28a%29.
So, log%2810%5E3%29%2Blog%2810%5E5%29=3log%2810%29%2B5log%2810%29. 8log%2810%29=log%2810%5E8%29, therefore, log%2810%5E3%29%2Blog%2810%5E5%29=log%2810%5E8%29

The two equations are related because the additions of logarithms produces the same operation as multiplication with regular numbers. Moreover, the conversion is also able to be done, to get the same result on both equation just by taking log/exponentiation, showing that the two are inverses.