Before working on task 2, please read the following reading:

Reading section4.1- Exponential Growth and Decayof the following textbook will help you in understanding the concepts better.

Yoshiwara, K. (2020).Modeling, functions, and graphs.American Institute of Mathematics.https://yoshiwarabooks.org/mfg/frontmatter.html

Write the logarithmic properties at each step to solve the following questions:

(i) Simplify using logarithmic properties,

\log_6 (\frac{216^x}{1296^x})\log_x6

(ii) Condense the complex logarithm into single term

\log(x + 1)^2 + log(2x - 1)^3 - log(x)^2 - log(2x - 1)^4 + 6log(x + 1)

(iii) Solve:

10e^{2x-3}=15e^{5x-7}

Task 3.A research laboratory has been conducting experiments on the rapid increase of cancer cells in an animal. They have observed that cancer cell growth increases by 2% every year with certain medication. Initially, in the year 2018, there were 232.26 units of these cells in the animal.

Using the above data, answer the following questions:

(i) Create a table to illustrate the yearly increase in cancer cells up to the year 2023.

(ii) Examine the table of values and identify the mathematical function that represents this growth pattern, specifying the key factors of the mathematical function.

(iii) Utilize this mathematical function to project the level of cancer cells in 10 years, assuming the growth rate continues at the same pace.

(iv) Illustrate the growth pattern by plotting a graph (Take scale 100units on X and Y-axes).

need help with the answers