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Logarithms – Answers to exercises – pg.10/10

Posted in Answers by Lia on 04/08/2013

pg. 123456, 789, 10

Exercises are on pg. 9

The theory is on pages 1 through 8

 

1.

a)  {log_5}25 =2;   b)  {log_7}343 =3;   c)  {log_23}12167 = 3;   d)  {log_25}625 =2;   e)  {log_9}6561 =4

 

2.

a) {log}10000 = 4;  b) {log}(10^6) = 6;  c) {log}10 = 1;  d) {log}(10^2) = 2;  e) {log}100 = 2

 

3.

a)  {{}{1}{}};   b)  {{}{2}{}};   c)  {{}{4}{}};   d)  {{}{0}{}};   e)  {{}{3}{}}

 

4.

a) {log_3}27 + {log_3}9 = 5;  b) {log_5}25 + {log_5}125 = 5;

c) {log_4}16 + {log_4}(a^3) + {log_4}(b^4) = 2 + 3{log_4}a + 4{log_4}b;

d) {log_7}(49) + {log_7}(b^2) = 2(1 + {log_7}b);

e) {log_2}8 + {log_2}(a^3) + {log_2}(b^6) + {log_2}(c^9) = 3(1 + {log_2}{a} + {log_2}(b^2) + {log_2}(c^3)) = 3(1 + {log_2}{a} + 2{log_2}{b} + 3{log_2}{c})

 

5.

a)  {log_2}64 = 6;   b)  {log_3}(27ab);  c)  2{log_4}(4{a^3});  d)  2{log_5}(5a{b^2});  e)  {log_7}(49c)

 

6.

a) {log_3}81 - {log_3}27 = 1;  b) {log_5}25 - {log_5}5 = 1;   c) {log_4}64 - {log_4}4 = 2;  d) {log_7}49 - {log_7}7 = 1;

e) {log_2}16 - {log_2}4 =2

 

7.

a)  {log_2}(32/8) = 2;   b)  {log_3}(27/3) = 2;  c)  {log_4}(64/16) = 1;  d)  {log_5}(25/5) =1;

e)  {log_7}(49/7)=1

 

8.

a) {{}{5}{}};  b) {{}{8}{}};   c) {{}{3}{}};  d) {{}{12}{}};  e) {{}{12}{}}; f){{}{1}{}};  g) {{}{1/2}{}};   h) {{}{1/3}{}};  i) {{}{1}{}};  j) {{}{4/3}{}}

 

9.

a) {{{log}27}/{{log}3}};  b) {{{log}25}/{{log}5}};   c) {{{log}30}/{{log}4}};  d) {{{log}49}/{{log}7}};  e) {{{log}10}/{{log}2}}

 

Exercises are on pg. 9

 

pg. 123456789, 10

 

 

 

 

 

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