Question

1)

Oblicz stosujac wzory na potegi

6²*6¹⁷=

(¼)⁷*(¼)⁷=

(-5)⁴*(-5)⁹=

3⁻²⁰*3²⁰=

5¹⁷/5²=

5²*5¹⁷=

(⅛)⁷/(⅛)⁷=

(-3)⁷/(-3)⁴=

5⁻²⁰/5²⁰=

(7⁵)⁵=

(8⁻¹)²=

5⁻²*5⁻²=

4²/4²=

2⁻²/4⁻²=

2 )

Oblicz stosujac wlasnosci logarytmow

log₂ 4=

log₄ 64=

log₃ 9=

log₂ 16=

log⅛ √8=

log √₂₇ 81=

log₇ 7²⁰=

log⁸/₅ 5=

log₉ 81²=

3)

Rozwiaz rownania

log x 36=2

log x 81=4

log x ¹/₁₂₅=3

log₂x 8⁷=7

Answer 1

1)

Oblicz stosujac wzory na potegi

6²*6¹⁷= 6¹⁹

(¼)⁷*(¼)⁷= [(¼)*(¼)]⁷ = [(½)⁴]⁷ = (½)²⁸

(-5)⁴*(-5)⁹= (-5)¹³

3⁻²⁰*3²⁰= 3⁰ =1

5¹⁷/5²=  5¹⁵

5²*5¹⁷ = 5¹⁹

(⅛)⁷/(⅛)⁷= (⅛)⁰ = 1

(-3)⁷/(-3)⁴=(-3)³

5⁻²⁰/5²⁰= 5⁻⁴⁰

(7⁵)⁵=7²⁵

(8⁻¹)²= 8⁻² = (2³)⁻² = 2⁻⁶

5⁻²*5⁻²= 5⁻⁴

4²/4²= 4⁰ = 1

2⁻²/4⁻²= 2⁻²/(2²)⁻² = 2⁻²/2⁻⁴= 2²

 

2 )

Oblicz stosujac wlasnosci logarytmow

log₂ 4=  2,      bo  2² = 4

log₄ 64= 3,      bo 4³ = 64

log₃ 9=  2,       bo 3² = 9

log₂ 16= 4,      bo 2⁴= 16

log⅛ √8= -½,    bo (⅛)^(-½) = 8^(½) = √8

log √₂₇ 81= 8/3 , bo (√27)^(8/3) =[ (27)^(½)]^(8/3) = 27^(4/3) =

                            = [(3)³]^(4/3)= 3⁴ = 81

                                 

log₇ 7²⁰= 20*log₇7 = 20*1 = 20

log⁸/₅ 5=

log₉ 81²= 2*log₉81 = 2*2 = 4

 

3)

Rozwiaz rownania

log x 36=2

  x² = 36

  x = 6

 

log x 81=4

 x⁴ = 81

 x⁴ = 3⁴

 x = 3

 

log x ¹/₁₂₅=3

 x ³ = 1/125

 x³ = (1/5)³

 x =  1/5

 

log₂x 8⁷=7

 (2x)⁷ = 8⁷

  2x = 8

  x = 4