Explain why log (5 • 2) is not equal to log 5 • log 2.

Question

 How are they not equal to one another. Please explain why. Thank you!

Answer 1

"log" is another name for exponent.

log (5 · 2) is the exponent on a product

What is the rule for exponents on like bases that are multiplied?

They are added.

log (5 · 2) = log 5 + log 2

Answer 2

^*Because the product rule for logarithms is

 

Log(A*B) = Log(A) + Log(B)

 

The way you've written would be this :

 

Log(5*2) = 1

 

Log(5)*Log(2) = 0.7*0.3 = 0.2

 

1 ≠ 0.2