Logs, Limits, & Forest Functions
A dryad whispers: log₂(8) = ?
3
Simplify √49.
7
Solve for x: 3x – 6 = 9.
x = 5
A fairy circle forms with radius 5 m. Find its area (π = 3.14).
78.5 m²
The Moon Goddess casts a silver beam at a 30° angle over the lake. If sin(30°) represents the reflection’s brightness, what fraction of full moonlight shines on the water?
0.5 half brightness
The spell grows as f(x) = 3x² + 2x – 1. Find f(–2).
7
A witch carves √(32x⁴y²) into stone. Simplify her rune.
4x²y√2
The magic circle forms where x² – 16 = 0. Find x.
x = ±4
A crystal prism has base area 12 cm² and height 10 cm. Find its volume.
120 cm³
A crystal compass aligns with the North Star, forming a 60° angle with the horizon. The guardian says its power equals cos(60°). How strong is its pull?
0.5 (half strength)
The elder tree doubles its height each year. If it starts at 2 m, express its height after t years as a function.
h(t) = 2(2)
The dragon’s flame burns at (3x²)³. Simplify.
27x⁶
The arch of a gate follows y = –x² + 4x + 5. Find the vertex.
(2, 9)
A forest obelisk casts a 15 m shadow when the sun’s angle of elevation is 45°. Find the obelisk’s height.
15 m
A mage draws a perfect sigil whose diagonal meets its base at a 45° angle. What is tan(45°), the ratio of its mystical rise to its run?
1 (perfect balance)
A rune states f(x) = 5x – 7. Find the inverse function.
f⁻¹(x) = (x + 7)/5
The enchanted mirror shows (x³y²)¹ᐟ³. Simplify the reflection.
x y(2/3)
A witch is given a problem to solve. Help her out! Solve for x: 2x² – 3x – 2 = 0.
x = 2 or –½
A spell creates a sphere with volume 905 cm³. Find its radius (π = 3.14).
≈ 6 cm
A dragon perches on a tower 3 m tall. Its shadow stretches 4.3 m across the mossy ground. Find the angle of elevation of the sun that awakens it. (tan θ = opposite/adjacent)
≈ 35°
The wisp approaches the forest’s edge: limₓ→2 (x² – 4)/(x – 2).
4
Solve for x: √(x + 3) = 5.
x = 22
A sorcerer’s spell peaks at vertex (3, –4) with equation y = a(x – 3)² – 4 passing through (4, –1). Find a and the full equation.
a = 3 → y = 3(x – 3)² – 4
A magical map shows a triangle with sides 7 m, 8 m, and 9 m. Use Heron’s formula to find its area.
≈ 26.83 m²
At midnight, a wizard charts the path of a comet. The angle between the horizon and the comet’s trail is θ, where sin(θ) = 0.7071. What constellation’s arc does the comet follow? (Find θ)
θ = 45° (The Circle of Balance)