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Logarithms – Exercises – pg.9/10

Posted in Math Problems by Lia on 04/08/2013

pg. 12345678, 9, 10

Answers  to  exercises are on pg.10

The theory is on pages 1 through 8

 

1. Write the exponential expressions as logarithmic expressions:

a)   5^2 = 25;  b)   7^3 = 343;  c)   23^3 = 12167;   d)   25^2 = 625;   e)   9^4 = 6561

 

2.  Calculate to following common logarithms:

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

 

3.   What is the “characteristic” value of  the following common logarithms:

a) {log}28b) {log}547;  c) {log}32678d) {log}2;  e) {log}3246

 

4.  Write the logarithms shown as a sum of  logarithms and solve them:

a) {log_3}(27*9);  b) {log_5}(25*125);   c) {log_4}(16{a^3}{b^4});  d) {log_7}(49{b^2});

e) {log_2}(8{a^3}{b^6}{c^9})

 

5.   Write the sum of the logarithms shown as  logarithms of a product and solve them:

a)  {log_2}4 + {log_2}16;   b)  {log_3}27 + {log_3}a + {log_3}b;  c)  {log_4}16 + {log_4}{a^6};

d)  {log_5}25 + {log_5}{a^2} + {log_5}{b^4};  e)  {log_7}49 + {log_7}c

 

6.  Write the logarithms shown as differences of  logarithms and solve them:

a) {log_3}(81/27);  b) {log_5}(25/5);   c) {log_4}(64/4);  d) {log_7}(49/7);  e) {log_2}(16/4)

 

7.  Write the differences of the logarithms shown as a logarithms of divisions and solve them:

a)  {log_2}32 - {log_2}8;   b)  {log_3}27 - {log_3}3;  c)  {log_4}64 - {log_4}16;  d)  {log_5}25 - {log_5}5;

e)  {log_7}49 - {log_7}7

 

8. Solve the logarithms:

a) {log_3}(3^5);  b) {log_5}(25^4);   c) {log_4}(4^3);  d) {log_7}(49^6);  e) {log_2}(16^3);

f){log_3}(root{5}{243});  g) {log_5}(root{4}{25});   h) {log_4}(root{3}{4});  i) {log_7}(sqrt{49});  j) {log_2}(root{3}{16})

 

9. Change the logarithms into common logarithms: 

a) {log_3}27;  b) {log_5}25;   c) {log_4}30;  d) {log_7}49;  e) {log_2}10

 

Answers  to  exercises are on pg.10

 

pg. 12345678, 9, 10

 

 

 

 

 

 

 

 

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