Logarithms

Rewrite to the other form

100

5³ = 125

What is Log₅(125) = 3

DOUBLE POINTS

200

Log₅(25)=2

What is 5²=25?  

300

7^x = 343

What is Log₇(343)=x?

400

Log_x(9)=-0.6

What is x^-0.6=9  

500

m^p=q

What is Log_m(q)=p?

Solve Exponentials

100

4+5^(x)=9

x=1.365

200

8^(x-2)=4

x=2.667

300

3*4^x-7=2

x=.792

400

3^(2x+4)-2=9

x=-.909

500

64^(2b-1)=1/16

b=1/6

DOUBLE POINTS

Expand Logarithm

100

Log₃(2x) 

Log₃(2) + Log₃(x) 

200

Log₄(64y) 

3 + Log₄(y) 

300

Log₆(5x²y) 

Log₆(5) + 2Log₆(x) + Log₆(y) 

400

Log₃(5x²/y³) 

Log₃(5) + 2Log₃(x) - 3Log₃(y) 

500

Log(100x²y)^1/2

1 + Log(x) + 1/2 Log(y) 

Solve Logarithms

100

log_3(27)=x

What is x = 3?

200

2log_5(x)=log_5(25)

What is x = 5? *Just 5 because we can't plug in -5*

300

log_4(5)+log_4(x+1)=log_4(3)

What is x = -2/5

400

log_8(2)=x

What is x = 1/3?

DOUBLE POINTS

500

log(2x)-log(10)=10

What is x = 55

Condense Logarithm

100

Log (5) + Log (10)

What is Log (50)

DOUBLE POINTS

200

Log (3x) - Log (2)

What is Log (3x/2)

300

Log (6) + Log (3x)

What is Log (18x)

400

2 Log (3) + 5 log (y) - log (x) 

What is Log (9y⁵/x) 

500

4 Log (J) - (Log (E) + 2 Log (H)) 

log(J^4/(EH^2))