Get the information you need from a community of experts on IDNLearn.com. Get accurate and comprehensive answers from our network of experienced professionals.
Sagot :
You can use the properties of logarithm to derive the simplified form of the given expression.
The simplification of the given expression requires the given below properties of logarithm
- [tex]log_a(b^c) = c \times log_a(b)\\\\[/tex]
- [tex]log_b(b) = 1[/tex]
What is logarithm and some of its useful properties?
When you raise a number with an exponent, there comes a result.
Lets say you get
[tex]a^b = c[/tex]
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
- [tex]b = log_a(c)[/tex]
Some properties of logarithm are:
[tex]log_a(b) = log_a(c) \implies b = c\\\\\log_a(b) + log_a(c) = log_a(b \times c)\\\\log_a(b) - log_a(c) = log_a(\frac{b}{c})\\\\log_a(b^c) = c \times log_a(b)\\\\log_b(b) = 1[/tex]
Using the above properties, to get to the simplified form of the given expression
The given expression is
[tex]log_b(b^{x+y})[/tex]
Using the property [tex]log_a(b^c) = c \times log_a(b)\\\\[/tex], we get
[tex]log_b(b^{x+y}) = (x+y)\times log_b(b)[/tex]
Using the property [tex]log_b(b) = 1[/tex], we get
[tex]log_b(b^{x+y}) = (x+y)\times log_b(b) = (x+y) \times 1 = x + y[/tex]
Thus,
The simplification of the given expression requires the given below properties of logarithm
- [tex]log_a(b^c) = c \times log_a(b)\\\\[/tex]
- [tex]log_b(b) = 1[/tex]
Learn more about logarithms here:
https://brainly.com/question/20835449
Answer:
logb(b^c)=c
Step-by-step explanation:
If you are doing this on edge it's C
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.
