Logarithms

Re-Write Logs

100

5³ = 125

What is Log₅ 125 = 3

200

4¹ = 4

What is Log ₄  4 = 1

300

7^X = 343

What is Log ₇  343 = X

400

X⁵ = 243

What is Log_x  243 = 5

500

M^P = Q

What is Log_M of Q = P

Re-Write Exponentials

100

Log₃ 2187 = 7

What is 3⁷ = 2187

200

Log₅ 25 = 2

What is 5² = 25

300

Log₈ X = 3.25

What is 8^3.25 = X

400

Log_X  -9 = 0.6

What is X^0.6 = -9

500

Log_A  B = C

What is A^C = B

Change of Base

100

log ₃ (3.3)

1.087

200

log ₂ (2.1)

1.070

300

log ₃ (83)

4.022

400

log ₄ 704

4.730

500

log ₁₄ (2.6)

0.362

Solving Logs

100

log_{3 (4x) = 2}

What is X = 9/4

200

ln(x² + 3) = ln(4)

What is x = -1 and x = 1

300

log₈ (x-5) = 2/3

What is x =9

400

ln(x) +ln(x+2) = ln(x+6)

x = 2 and x = -3

500

log₂ (x+5) - log₂ (x-2) = 3

What is x = 3

Properties of Logs

100

Expand the Logarithmic Expression:

log₄ (4x)

log₄ 4 + log₄ x

200

Expand the Logarithmic Expression:

ln(3x⁴)

ln(3) + 4ln(x)

300

Condense the Logarithmic Expression 

log₄ (7) - log₄ (10)

log₄ (7/10)

400

Condense the Logarithmic Expression:

6ln (x) + 4ln (y)

ln (x⁶y⁴) 

500

Expand the Logarithmic Expression:

ln(6x²/y⁴)

ln(6) + 2ln(x) - 4ln(y)