Brittney's Board

Logarithms

100

Simplify:

log_bb^b

What is b?

200

Simplify

log₄16²

What is 4

300

Solve

log₅6x=-3

What is x = 1/750

400

Solve

log(2x+8) - log(3x-2) = log10

What is x = 1?

500

Solve

ln(x²-1) = pi

What is x = +/- sqrt((e^pi)+1)

Exponentials

100

x³=64

What is x=4

200

5^-x=625

What is x = -4

300

x³ = 4x⁵

What is x = 1/2

400

5^x+2=25^3x-1

What is x = 4/5

500

27^{x^2 -16} = (1/243)^-9x

What is x = -1, 16

Trigonometry

100

sin(5(pi)/2)

What is 1

200

Given cos(x) = 5/13, csc(x)

What is 13/12

300

Simplify cosx-cosxsin²x

What is cos³x

400

All solutions to tanx=1 for 0<x<2pi

What is x = pi/4, 5pi/4

500

Simplify

(cscx + cotx)/(tanx+sinx)

What is cotxcscx

Factoring

100

Solve

x²-9x=-14

What is x = 2, 7

200

Factor 

x⁴-9x³-4x²+36x

What is x(x-9)(x-2)(x+2)

300

Solve by Completing the Square

2x²-8x-15=0

What is x = 2 - sqrt(23/2) , x = 2 + sqrt(23/2)

400

Solve by factoring

x²-10x^(3/2)+25x

What is x(x^(1/2)-5)² , x = 0, 25

500

Factor

6x⁶+42x³-48

What is 6(x-1)(x+2)(x²+x+1)(x²-2x+4)