Logarithms

Expanding

100

log₇(3x)

log₇3 + log₇x

200

log₂(6x)³

3log₂6 + 3log₂x

300

log₅(2x⁴y)

log₅2 + 4log₅x + log₅y

400

log₄(7x/2)²

(2log₄7 + 2log₄x) - 2log₄2

500

log₂(4x²/3x)

(log₂4 + 2log₂x) - (log₂3 + log₂x)

Condensing

100

7log₃x 

log₃x⁷

200

xlog₂3 - log₂4

log₂(3^x/4)

300

(2x)log₃7 - 3log₃x

log₃(7^2x/x³)

400

log₂x- 3log₂y + 3log₂x

log₂(x⁴/y³)

500

4log₄(x-2) - log₄x

log₄((x-2)⁴/x)

Rewriting

100

log₂(8) = 3

2³=8

200

log_x2=4

x⁴=2

300

log₃(x) = 5

3⁵ = x

400

4² = x+2

log₄(x+2) = 2

500

log_4x(x+4) = 3

(4x)³ = x+4

Evaluating (Level 1)

100

log₅24 = log₅(x+2)

24 = x+2

24-2 = x

x= 22

200

log₆4x = log₆100

4x = 100

x = 100/4

x = 25

300

2log₂x = 4

2⁴ = x²

16 = x²

x=4

400

log₂(5x+3) = 3

2³=5x+3

8=5x+3

8-3=5=5x

x=1

500

log₂(x+17) = 3log₂2

x+17 = 2³

x+17 = 8

x = -9

Evaluating (Level 2)

100

log(3x − 2) = 2

10²=3x-2

100=3x-2

102=3x

x= 102/3

x=34

200

log₅(2x+3)=2

5²= 2x+3

25=2x+3

25-3=2x

22=2x

x=11

300

logx=1−log(x−3)

log(2) + log(x-7) = 1

log(2x-14) = 1

10¹=2x-14

10+14=2x

24=2x

x=12

400

log(x) + log(x-1) = log(4x)

log (x *(x-1)) = log(4x)

log(x²-x) = log(4x)

x²-x=4x

x²=5x

x=5

500

ln(5) + ln(x) - ln(6) = ln(5)

ln(5x) - ln(6) = ln(5)

ln(5x/6) = ln(5)

(5x)/6 = 5

5x = 6(5) = 30

x=30/5 = 6