Radical Expressions!
Exponential Equations
A Pile of Logs
Logs and Little Numbers
Graphs and More Logs
100
Find the value of the expression 2(-3)4
2(-3)4 = 2(81) = 162
100
Solve 23x-1 = 42x+1
2^(3x-1) = 4^(2x+1) → 2^(3x-1) = (2²)^(2x+1) → 2^(3x-1) = 2^(4x+2) → 3x-1 = 4x+2 →
x = -3
100
Which of the following logarithmic expressions have been evaluated correctly? Select all that apply
A. log₃ 9 = 2
B. log₅ 125 = 4
C. log₂ 16 = 4
D. log₁₀ 1000 = 3
A, C, D are correct
100
Which shows the expression 2 log x - log(x³) written as a single logarithm?
A. log(x²/x³)
B. log(x²) - log(x³)
C. log(1/x)
D. log(2x - x³)
C. log(1/x)
100
Which graph shows the function
f(x) = sqrt (x-3) +2 ?
A.
B.
C.
D.
A
200
Find the value of the expression -4(2)5
-4(2)5 = -4(32) = -128
200
Solve 5x+2 = 25x-1
5^(x+2) = 25^(x-1) → 5^(x+2) = (5²)^(x-1) → 5^(x+2) = 5^(2x-2) → x+2 = 2x-2 →
x = 4
200
Which of the following logarithmic expressions have been evaluated correctly? Select all that apply:
A. log₄ 64 = 3
B. log₆ 36 = 2
C. log₂ 32 = 6
D. log₁₀ 100 = 2
A, B, D are correct
200
Which shows the expression 4 log y - 2 log(x²) written as a single logarithm?
A. log(y⁴/x⁴)
B. log(4y - 2x²)
C. log(y⁴) - log(x⁴)
D. log(1)
A. log(y⁴/x⁴)
200
Draw the graph of f(x)= 2 (x)1/3
300
What is the simplified form of √(72x³y²)
√(72x³y²) = √(36x²y² • 2x) = 6xy√(2x)
300
For the function f(x) = 0.25 • (4)x + 3, identify the y-intercept and asymptote.
y-intercept: f(0) = 0.25(1) + 3 = 3.25; asymptote: y = 3
300
What is the solution to the equation log₃(2x - 1) = 4?
log₃(2x - 1) = 4 → 2x - 1 = 3⁴ → 2x - 1 = 81 →
x = 41
300
Solve the equation 3x+2 = 92x-1
3^(x+2) = 9^(2x-1) → 3^(x+2) = (3²)^(2x-1) → x+2 = 4x-2 →
x = 4/3
300
Evaluate log520 (round to the nearest hundredth).
1.86
400
What is the simplified form of √(98a⁴b³)
√(98a⁴b³) = √(49a⁴b² • 2b) = 7a²b√(2b)
400
For the function f(x) = 2 • (3)x - 1, identify the y-intercept and asymptote.
y-intercept: f(0) = 2(1) - 1 = 1; asymptote: y = -1
400
What is the solution to the equation log₄(x + 5) = 3?
log₄(x + 5) = 3 → x + 5 = 4³ → x + 5 = 64 →
x = 59
400
Solve the equation 8x-1 = 43x+2
8^(x-1) = 4^(3x+2) → (2³)^(x-1) = (2²)^(3x+2) → 3(x-1) = 2(3x+2) →
x = -7/3
400
Evaluate log164096 (round to the nearest hundredth).
3