Properties of logarithms

Evaluating Logs

2

Is the evaluation of  log ₂ (8)

What is 3 ?

3

Is the evaluation of  log₃₇(1)

What is 0 ?

5

Is the evaluation of  log ₅ ( ¹/₁₂₅ )

What is -3 ?

7

Is the evaluation of  log ( 1,000,000,000 )

What is 9 ?

11

Is the evaluation of  log ₁₀₀ (10,000 )

What is 2 ?

Expand, using Laws of log

2

Is the expansion of the expression log _a (xy²)

What is log _a x  +  2 log _a y ?

3

Is the expansion of the expression log _a (^x/_y³)

What is  log_ax - 3log_ay  ?

5

Is the expansion of the expression log _a (xy³/_z4)^1/₂ 

What is ¹/₂ log_ax + ³/₂log_ay - 2log_az  ?

7

Is the expansion of the expression ln (^3x/_yz)

What is  ln 3 + ln x - ln y - ln z  ?

11

Is the expansion of the expression  log _a x²y⁵z.

What is  2log_ax  + 5log_ay  + log_az  ?

Condense, using laws of log

2

Is the expression log_ax - log_ay  as a single term

What is  log_a(^x/_y)  ?

3

Is the expression 3log_ax + 4log_ay  as a single term

What is  log_ax³y⁴  ?

5

Is the expression ¹/₄log_ax - ³/₄log_ay  as a single term

What is  log_a(^x/_y3)^1/4   ?

7

Is the expression 3log_ax - 2(log_ay + log_az) as a single term

What is  log_a(x³ / y²z²)  ?

11

Is the expression 3log_ax + 2log_ay - log_az as a single term

What is log_a( x³y²/z ) ?

Solve the equation

2

Is the solution of the equation 

 log₄(x + 10 )  = log₄ ( 8 - x )

What is x = 1 ?

3

Is the solution of the equation 

 log₆(2x - 3)  = log₆ 24  - log₆ 3

What is  x = ¹¹/₂  ?

5

Is the solution of the equation 

ln x² = ln (12 - x )

What is x = -4, or x = 3  ?

7

Is the solution of the equation 

 log₂ (x+7) + log₂ x = 3

What is  x = -8, or x = 1  ?

11

Is the solution of the equation 

 log₃(x+3) + log₃(x+5)=1

What is x = -2  ?

...and even more equations

2

Is the solution of the equation 

 log₃(x - 4)=2

What is  x = 13 ?

3

Is the solution of the equation 

 log₆(2x-3)  = log₆ 24  -  log₆4

What is  x = ⁹/₂  ?

5

Is the solution of the equation 

 log x² = -4

What is  x = ¹/₁₀₀  ?

7

Is the solution of the equation 

 log₂(-x) + log₂ ( 2 - x )=3

What is  x = -2 ?

11

Is the solution of the equation 

 log₃(-x)  + log₃ (8 - x) = 2

What is  x = -1  ?