The proof for the product property of logarithms requires simplifying the expression logb(bx+y) to x + y. Which property is used to justify this step?

Question

asked Oct 5, 2021 121k views

2 Answers

Harry Bloom · Answer 1 · 2021-10-09T10:45:54+0000

Answer:

log_bb^c=c

Explanation:

We are given that

log_bb^(x+y)=x+y

We have to find the property which is used to justify this step.

We know that

$e^(x+y)=e^x\cdot e^y}$

Using the formula

$log_b(b^x\cdot b^y)}=log_bb^x+log_bb^y$

By using the formula

$log(m\cdot n)=log m+log n$

log_bb^(x+y)=x+y

By using the property

log_bb^c=c