Question

1.Вычислить:

Log3 4 - log3 16 + log3 4/9;
2. Вычислить:

2 log7 27 – log7 81-2 log7 21

3. вычислить:

2 log2 8 +log2 15/4 – log2 15

4. log3 7 * log4 81 * log7 2

5. вычислить:

Lg3(log325+log32 - log35)

Answer 1

1. Log3 1/4 +Log3 4/9= -2

2.log7 (729/{441*81}) = -2

3.log2 240-log2 15 = 4

4.(log7 2 / log7 3) *1/2log2 81 = 1/2 * (log2 81/log2 3) = 2

5.----------

Answer 2

 

 

 

 

1)  Log3 4 - log3 16 + log3 4/9= Log3 4/ 16 + log3 4/9=Log3 ((4/16)*( 4/9))= Log3 1/9= 

  Log3 (3)^-2=  -2

 

2)  2 log7 27 – log7 81-2 log7 21=log7 27^2 / 81-2 log7 21=  log7 729/ 81- log7 21 ^2=  log7 9- log7 21 ^2 =  log7 (9/ 441)=  log7 (1/ 49) =  log7 (7^-2)=-2 

 

3)   2 log2 8 +log2 15/4 – log2 15=log2 (8^2*(15/4)) – log2 15=  log2 ((64*15)/4) – log2 15 =

    log2 (16*15) – log2 15 =   log2 ((16*15)/15)=   log2 (16)=   log2 (2^4)=4 

 

4)   log3 7 * log4 81 * log7 2=   log4 81 * log7 2*1/ log7  3=  log4  3^4 *( log7 2/ log7  3 )= 

  4* log4 3 * log3 2=4*  log3 2*(1/  log3  4) = 4*  log3 2*(1/  log3  2^2) = 4*  log3 2*(1/ 2 log3  2)=    (4*  log3 2)/ (2 log3  2) =4/2=2

 

5)  Lg3(log3 25+log3 2-log3 5) =  Lg3(log3 (25* 2)-log3 5)=  Lg3(log3 50/ 5) =  Lg3*log3 10 =   log10  3* log3 10=  log10  3/ log10  3=1