HA2 SEM2 practice 3

If [math]\dfrac{(2x^3y^5z)^2}{12x^7y^4z^{-3}}=ax^by^cz^d[/math] where [math]a, b, c[/math], and [math]d[/math] are constants, what is [math]a+b+c+d[/math]?

Solve the following equations. If you have two or more answers, write the biggest one.

(a) [math]9^{2x+1}=27\cdot3^{6x}[/math]

(b) [math]x^{\frac{3}{4}}=27[/math]

Solve the equation system: [math]\begin{cases}\dfrac{1}{4^{-x}}=16^{2y+5}\\11^y\cdot11^x=121^{2+y}\end{cases}[/math]

Consider the geometric sequence [math]72, -36, 18, -9[/math]. If the sequence can be written as [math]a\cdot r^{n-1}[/math] where [math]a[/math] and [math]r[/math] are constants and [math]n[/math] is a positive integer, what are [math]a[/math] and [math]r[/math]?

Find the product of all possible values of [math]r[/math] in the geometric sequence where [math]a_{12}=36[/math] and [math]a_{10}=4[/math].

If [math]5+8+11+14+17+20=\displaystyle{\sum^{5}_{k=1}a_k}[/math], what is [math]a_k[/math]?

(Calculator) Find the geometric series [math]2+10+50+\cdots+31250[/math]

(Calculator) If Lindsay’s parents put $10,000 in a saving acount upon her borth, what annual interest rate [math]r[/math] would be necessary in order to have $25,000 upon her high school graduation (when she is 18 years old)?

(Calculator) $8000 is to be placed into a bank at [math]3.8\%[/math] annual interest compounded continuously. How long will it take, in years, to triple the amounr in the account? Round to the nearest integer.

Solve the following equations. If you have two or more answers, write the smallest one.

(a) [math]\log x+\log(x-15)=2[/math]

(b) [math]\log_2(\log_4(\log_3x))=-1[/math]

If [math]f(x)=\dfrac{(x+1)^2(x-2)(x+3)}{(x+1)(x-2)^2}[/math]

Solve the rational equation [math]\dfrac{1}{x^2-4x}+1=\dfrac{x-6}{x}[/math]. If you have two or more answers, write the biggest one.

[math]\log\left(\dfrac{a^2b^3}{c^4d^5}\right)=[/math]