2.6 Logarithms

Re-Write Logs

100

5³ = 125

Log₅ = 3

200

4¹ = 4

Log ₄ 4 = 1

300

7^X = 343

What is Log ₇ 343 = X

400

X ⁵ = 243

 Log_X 243 = 5

500

M^P = Q

Log _M Q = P

Re-Write Exponentials

100

Log₃2187 = 7

3⁷ = 2187

200

Log ₅ 25 = 2

5² = 25

300

Log ₈ X = 3.25

8^3.25 = X

400

Log_X -9 = 0.6

X^0.6 = -9

500

Log _A B = C

 A^C = B

Solving Exponentials

100

solve: x⁵ = 243

What is x=3

200

Solve: x⁵=32x

 x = 2.378 (3d.p)

300

Solve: 0.8 x (1.05)^y = 15

y = 60.078 (3d.p)

400

Solve: 81^x-2 = 27^x

x = 8

500

Solve: 6^2x+1 = 4^x-1

x = -log(24)/log(9) = -1.446 (3 d.p)

Solving Logs

100

Log₃27= X

x=3 

200

Log₄16 = x

What is x = 2

300

Log_x 4 = 3.5

x = 1.486 (3d.p)

400

Log₈16 = X

What is x = 4/3

500

Log_x(1/625) = -4

x = 5

Properties of Logs

100

Log (5) + Log (10)

Log (50)

200

Log (30) - Log (20)

What is Log (3/2)

300

Log (6) + Log (3x)

Log (18x)

400

2 Log (7)

Log (7²)

500

4Log J - Log E

Log (J⁴/E)