Given:
Consider the equation is:

To prove:
by using the properties of logarithms.
Solution:
We have,

Taking left hand side (LHS), we get

![\left[\because \log_ab=\dfrac{\log_x a}{\log_x b}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbecause%20%5Clog_ab%3D%5Cdfrac%7B%5Clog_x%20a%7D%7B%5Clog_x%20b%7D%5Cright%5D)

![[\because \log x^n=n\log x]](https://tex.z-dn.net/?f=%5B%5Cbecause%20%5Clog%20x%5En%3Dn%5Clog%20x%5D)

![\left[\because \log_ab=\dfrac{\log_x a}{\log_x b}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbecause%20%5Clog_ab%3D%5Cdfrac%7B%5Clog_x%20a%7D%7B%5Clog_x%20b%7D%5Cright%5D)

Hence proved.
Answer:
4+3x
It's pretty straight forward, you have the number 4 that is added to the rest of the expression because sum is addition, and the product of 2 numbers is multiplication so it would make 3(x) or 3x, which results in 4+3x.
Answer:
standard form: y = -x^2 + 15x
Answer:
Interval [b,c] and interval [c,d]
Step-by-step explanation:
a(-5,0)
b(-1,2)
c(4,3)
d(11,4)
The average rate of change is the the total rise over the total run.
The Rise means the vertical increase and the Run means horizontal incease.
For interval [a,b]
rate of change is 
For [b,c]

For [c,d]

Answer:
Step-by-step explanation:
12t2 - 6t