Logarithms

Converting between exponential and logarithmic form

100

3³=4x     Convert to Log

log₃(4x)=3

200

10²=x²+3x-17  Convert to Log

log(x²+3x-17)=2

300

(2x+7)^3x+5=x²+x+17 Convert to Log

log_2x+7(x²+x+17)=3x+5

400

e³=2x   Convert to ln

ln(2x)=3

500

e^3/5=2x  Convert to ln

ln(2x)=3/5

Evaluating logarithms

100

log₄ 16 Evaluate

2

200

log₃27  Evaluate 

3

300

log₇ 1/343  Evaluate

-3

400

log₇ 1/49

-2

500

log₆₄ 1/4 Evalute

 -1/3

Condense logarithms

100

log₃-log₈ Condense

log 3/8

200

4log3-4log8 Condense

log 3⁴/8⁴

300

log7 - 2log 12 Condense

log 7/12²

400

2 log 7 / 3 Condense

log cube root 7²

500

ln x - 4ln y Condense

ln x/y⁴

Logarithmic equations

100

log 5x= log(2x+9) Solve for x

3

200

log (10-4x) = log (10-3x) Solve for x

0

300

log (4k-5)= log (2k-1) Solve for k

2

400

log -m + 2 = 4 Solve for m

-100

500

log x - log 2= 1 Solve for x

20

Exponential equations that require logs

100

3^b=17 Solve for b

2.5789

200

6^r=51 Solve for r

2.1944

300

9ⁿ⁺¹⁰+3=81 Solve for n

-8.0172

400

16^n-7+5=24 Solve for n

8.062

500

5*6^3m=208 Solve for m

0.2579