9.3/9.4 Quiz Review

Change of Base

100

Evaluate log₂6 using the Change-of-Base formula.

What is 2.585?

200

Evaluate log₅35 using the Change-of Base formula.

What is 2.209?

300

Evaluate log_1/25 using Change-of-Base formula.

What is -2.322?

400

Evaluate log₁₆0.63 using the Change-of-Base formula.

What is -0.167?

500

Evaluate log_3/424 using the Change-of-Base formula.

What is -11.047?

Expand Logs

100

Expand log₂(5/3)

What is log₂5-log₂3?

200

Expand log₂42

What is log₂6 +log₂7?

300

Expand log₂3a⁴

What is log₂3+4log₂a?

400

Expand ln (x^1/2/7)

What is 1/2 lnx - ln 7?

500

Expand log (10x²/y³)

What is 1+2logx - 3logy?

Condense Logs

100

Condense ln7 + lnx

What is ln7x?

200

Condense log₃13 + log₃y

What is log₃13y?

300

Condense 4ln x - 4lny

What is ln x⁴/y⁴?

400

Condense 3lnx - ln(x+3) + 2lny

What is ln x³y²/(x +3)

500

Condense 1/2log₃x - 2log₃(y+8)

What is log₃(sqrt(x)/(y+8)²)?

Solving Exponential Equations

100

Solve 25e^-0.3x=12

What is x = 2.447?

200

Solve for x: 2^x - 3 = 29

What is x = ln 32/ ln 2 = 5?

300

Solve for x: e^4x = e^{(x^2) + 3} 

What is x= 1, 3?

400

Solve for x: 3e^-5x = 132

What is x = ln44/-5 = -0.757

500

Solve for x: 1025/(8+e^4x) = 5

What is x = ln(197)/4 = 1.321

Solving Logarithmic Equations

100

Solve for x: lnx - lnx² =1/2

What is x = 0.607?

200

Solve for x: log(2x-1) = log(4x-3)

What is x = 1?

300

Solve for x: lnx + ln(x-3) = 1

What is x = 3.729?

400

What is logx + log(x-15) = 2

What is x = 0.064?

500

Solve for x: log₈(x-1) = log₈(x-2) - log₈(x+2)

What is no solution?