# BARC Quiz 1: Solution and Q&A

## Quiz 1 - Part 1

- Find $\ln A$ if $\log_5 A = 4$.
- $\log_3 11 = x$. What is the value of $x$?
- Given $\log_a 2 = x$, $\log_a 5 = y$, and $\log_a 6 = z$, express $\log_a 0.15$ in terms of $x$, $y$, and $z$.
- Solve for $x$ from $7^{2x - 1} = 3^{x + 1}$
- Find $x$ in the expression $\left( \dfrac{x}{5} \right)^{2/3} = 5$.

## Quiz 1 - Part 2

- Find the sum of the coefficient of the variables in the expansion of $(2x + 4y - 3)^5$.
- Find the 4
^{th}term in the expansion of $(x^3 + y^2)^4$. - The middle term in the expansion of $(x^3 + 4)^{10}$ is ...

## Quiz 1 - Part 3

- Find the product of the roots of the quadratic equation $4x^2 + 2x - 1 = 0$.
- There were 150 mg of a radioactive material stored at the start of the year 2000. The material has a half-life of 15 years. How much radioactive material will there be at the start of 2040?