Algebra 2 Properties of Logs, Common Logs, and Base e and ln

Solve:

log (x - 1) - log (x - 2) = log 5

• 7

• 4/9

• 9/4

• 1/7

Solve the following for 'x';
log₆(3x - 2) = log₆(5x - 8)

• x = 3
• x = 2
• x = -1
• No Solution

Use multiple log properties to write as a single log:
log₂x -  5log₂y

• log₂(x/y⁵)
• log₂(xy⁵)
• log₂(x/y)⁵
• log₂(x/5y)

Evaluate log₅  20 to the third decimal place

• 0.537
• 2.996
• 1.301
• 1.861

Evaluate log₄1

• 1
• 0
• 4
• undefined

Solve

• -.20

• .60

• .20

• -.6

 $\log\left(\frac{m^3}{n}\right)$  Use the properties of logs to rewrite

• logm-log3-logn

• 3logm+logn

• 3logm-logn

• 3log(m-n)

ln (5x + 6) = 5

• 154.413

• 30.883

• 147.213

• 28.483

Rewrite e^x = 9 using a logarithm

• ln x = 9

• ln 9 = x

• log_x e = 9

• log₉ x = e

3e^2x + 10 = 25

• {-3.940}

• {1.228}

• {0.451}

• {0.805}