Solve for x in the given equation.

1/512 = x^-9 

Provide the domain and range of the function by graphing it.
f(x) = 11^{x +3} +27

Graph the following function by graphing first its parent function, f(x) = log x, and performing transformation. Determine its vertical asymptote, domain, and range: g(x) = log (x + 3)

Graph the following equations: f(x) = 2^x and g(x) = log₂ x

Evaluate the given expression using common or natural logarithms and a calculator up to four decimals. 

log₇ 31

Solve the logarithmic equation for x and provide an exact solution:

log₄ (x² - 225) - log₄ (x + 15) = 1

Draw the graph of the following function. $f\left(x\right)=\left(\frac18\right)^{-x}$

Determine whether the straight line 6x - 5y = 11 intersects the given circle.

x² + y² = 49

For the given rational expression, write in its partial fraction decomposition form.

(x² - 2x + 1)/x(x + 1)(x - 1)

Graph the following ellipse and determine its foci: x²/16 + y²/49 = 1

Using the provided equation, find the parabola's vertex, focus, and directrix. Then, graph the parabola.
(y + 8)² = 8(x + 6)

Without completing the square, determine whether the equation represents a parabola, circle, ellipse, or hyperbola.

$121x^2+49y^2+1452x-1764y+14303=0$

Determine the graph that the equation represents.

$x^2+y^2=147$

Write the equation that describes the nth term of the following arithmetic sequence: 17, 9, 1, -7,...

Then, use the equation to determine the 25th term of the sequence.

Evaluate the specified sum for the given geometric sequence.

Enumerate the first three terms of the resulting expression if you are to apply binomial expansion to the following. (x + 13)⁶

In a certain country, there are only two weathers - it's either sunny or rainy. Assuming that the probability of a day being rainy is 1/2, what is the probability that it will be sunny on eight successive days?

For the general term of the sequence given, write its first four terms: $a_n= -13(n +2)!$