Logarithmic Equations

Log to Exponential

100

log_nm=-6  

n^-6=m

200

log₁₃ 169=2

13² = 169

300

log_y 76=x

y^x =76

400

log₁₄ 1/196= -2

14^-2 = 1/196

500

log_1/6 1/216 = 3

(1/6)³ = 1/216

Exponential to Log

100

12² =144

log₁₂ 144=2

200

81^1/2 =9

log₈₁ 9= 1/2

300

6^1/2 = √6

log₆ (√6) = 1/2

400

10^-4 =1/10,000

log₁₀ 1/10,000= -4

500

y^2/3 = x

log_y x= 2/3

Evaluating Logs

100

y= log(1000)

y= 3

200

y= log(1,000,000)

y=6 

300

y= In(500)

y= 6.21

400

y= log₆₄ 1/4

y= -1/3

500

In(√2)

.347

Expand Logs

100

log₆ u/v 

log₆ u − log₆ v

200

 log₇ 5 ⁴ 

4 log ₇ 5

300

log (a ⋅ b)

 log a + log b

400

 log_{4 u}⁶

6log ₄ u

500

log ₆ (3 ⋅ 11)⁶ 

 6 log₆ 3 + 6 log₆ 11

Solving Logs

100

6+ln x=10

e⁴=x

200

2 ln(x+1)=10

e⁵-1=x

300

2 ln x+3=7

e²=x 

400

ln(4x-10)-6=-5

e+10/4

500

10-4 ln (9-8x)=6

e-9/8