What are the cut points of a rational function?

True or False. The graph of a rational function may intersect a horizontal asymptote.

To write and solve the system of linear equations to find the price of 1 cup of dried fruit and 1 cup of almonds.
Given: A small bag of trail mix contains 3 cups of driedd fruit and 4 cups of almonds. A large bag contains ${\displaystyle 4\frac{1}{2}}$ cups of dried fruit and 6 cups of almonds.

How does $7\log (8x)=7\ln 8x$
I was working on some math homework with a program called scientific notebook. I was check that
I was writing something correctly.
The original equation is $(\log (x^4)+\log (x^5))/\log (8x)=7$
I then converted it to $\log (x^{(4+5)})=7\log (8x)$
I was expecting to get $\log ((8x{)}^7)$ when I entered the $7\log (8x)$ into the program to evaluate. Can someone please explain this to me?

Decide if the equation represents exponential growth or decay. Explain your answer. $y/2^x=3/2$

What is the standard form of ${\displaystyle y=(x-x^2)(x-8)-{(x+3)}^3}$?

Finding the value of an expression with logarithms
Given that ${\log }_{b}a=0.74$ and ${\log }_b(a-1)=0.65$ find the value of the following expression:
${\log }_b(a^4-1)-2{\log }_b(a^2+1)+{\log }_b(a^3+a)-{\log }_b(a+1)$
I tried using log laws to no avail. Help Is much appreciated!

In the year 2004, a total of 7.9 million pasengers took acruise vacation.${}^2$ The global cruise industry has beengrowing at approximately 10% per year for the last 10 years, assumethat this growth rate continues
a) write a formula to approximate the number, N. ofpassengers in millions t years after 2004.
b)how many cruise passengers are prdicted in the year 2010?Approximately how many passengers went on a cruise in the year2000?