UNIT 6B Review Algebra 2 H

Basic Logarithms

100

Log ₁₀ (1/10) = ?

-1

200

Log ₃ (sqrt(3)) = ?

1/2

300

Log ₈₁ 0 = ?

No solution

400

Log ₂₇ 3 = ?

1/3

500

2^{Log 2 (3)} = ?

3

Properties of Logarithms

100

Expand the logarithmic expression:

Log 1000x = ?

3 + log x

200

Expand the logarithmic expression:

Ln (e⁸ / 13) = ?

8 - ln 13

300

Expand the logarithmic expression:

Ln (4th root of x) = ?

1/4 ln x

400

Rewrite Log ₈ 13 in base e

ln 13 / ln 8

500

Expand the logarithmic expression:

Log (100z)

2 +  log z

Logarithmic Equations

100

Solve for x:

Log ₄ (x + 7) = 2

x = 9

200

Solve for x:

Log ₆ (x + 8) + Log ₆ (x + 3) = 1

x = -2

300

Solve for x:

Log ₆ (x + 28) - Log ₆ (x-7) = 2

x = 8

400

Solve for x:

ln x + ln (x - 2) = ln 3

x = 3

500

Solve for x:

Log (5x - 4) = Log (x + 3) + Log 6

No solution

Exponential Equations

100

Solve for x:

3^x = 107

x = 4.25

200

Solve for x: 

7^0.9x = 519

x = 3.57

300

Solve by expressing each side as the power of the same base:

3^{(x-6 / 8)} = sqrt(3)

x = 10

400

Solve for x:

5^{3x + 6} = 5^{x - 7}

x = -13/2

500

Solve for x:

e^2x - 8e^x + 7 = 0

x = 0 

&

x = 1.95

Compound Interest

100

$40,000 is invested at 5% and compounded annually for 5 years.

What is the final balance?

$51,051.26

200

$3000 is invested at 8% and compounded continuously for 7 years.

What is the final balance?

$5252.02

300

What investment would reach a final balance of $50,000 if it was compounded continuously at a rate of 7% for 19 years?

$13,223.86

400

How long would it take for $50,000 to reach $125,000 if it was compounded at 10.4% daily?

8.8 years

500

How long would it take for a $2800 investment compounded at 18.3% continuously to triple in value?

6 years