The logarithmic function — Paper 2 · IGCSE Mathematics - International 0607

16 Simplify. 2 2 log 3 - 3 log 2 + 2 log 3 … [3]

3 marks

Mark scheme: 16 1 3  3 2  2  2  log or − log2 final answer or better M2 for log   ×   2   2 3  3    or M1 for one correct use of log rules.

This question in 0607/21 May/June 2017

14 Find the value of x when 5 log 2 - log 8 = logx . x = … [2] Question 15 is printed on the next page.

2 marks

Mark scheme: 14 4 2 a M1 for log 25 or log or 3log2 or log23 8

This question in 0607/22 May/June 2017

15 (a) logk = 2log3 - 5log2 Find the value of k. k = … [2] (b) log2 p = -1 Find the value of p. p = … [1]

3 marks

Mark scheme: 15(a) 9 2 M1 for correct use of a log b = log b a 32 p or log p − log q = log q 15(b) 0.5 oe 1

This question in 0607/22 Oct/Nov 2017

14 (a) Write down the value of log 9 3 . … [1] (b) 2 log 2 + log 11 = logx . Find the value of x. x = … [2] Question 15 is printed on the next page.

3 marks

Mark scheme: 14(a) 1 1 or 0.5 2 14(b) 44 2 M1 for correct use of 2log2 = log2 2 oe or for correct use of log p + log q = log pq

This question in 0607/21 May/June 2018

15 (a) Solve 3 log 2 - 2 log 5 = logx . x = … [3] 1 (b) Solve log y 4 = . 3 y = … [1]

4 marks

Mark scheme: 15(a) 8 3 M1 for correct use of nloga = logan or 0.32 M1 for correct use of loga – logb = log(a ÷ b) 25 15(b) 64 1

This question in 0607/23 May/June 2018

14 (a) Find the value of n when log 5 + log 3 - log 2 = logn . … [1] (b) Find log 3 (3 1.4 ) . … [1]

2 marks

Mark scheme: 14(a) 7.5 1 14(b) 1.4 1

This question in 0607/22 Oct/Nov 2018

14 (a) Find the value of log 25 5 . … [1] (b) Simplify log 63 - 2 log 3 . … [2]

3 marks

Mark scheme: 14(a) 1 1 or 0.5 2 14(b) log 7 2 M1 for correct use of logan = nloga or log(a ÷ b) = loga – logb

This question in 0607/21 May/June 2019

19 (a) 2 log x = 3 log 4 Find the value of x. x = … [2] (b) log x + log u - log v = log p Find p in terms of x, u and v. p = … [1]

3 marks

Mark scheme: 19(a) 8 2 B1 for answer 23 or M1 for log( x 2 ) or for log(4 3 ) seen 19(b) xu 1 v

This question in 0607/22 May/June 2019

13 Solve the equation. 3 log x - log 4 = 4 log 2 x = … [3] Questions 14 and 15 are printed on the next page.

3 marks

Mark scheme: 13 4 3 M2 for log x 3 = log(2 4 × 4) or M1 for one correct use of rules of logs

This question in 0607/22 Oct/Nov 2019

12 3 log y = 2 log x - log w Find y in terms of x and w. y = … [3]

3 marks

Mark scheme: 12 2 3 M1 for 2logx = logx2 or 3logy = logy3 x 3 (implied by cube root in answer). w M1 for correct use of  p  log p − log q = log    q 

This question in 0607/21 May/June 2020

13 Solve. (a) log x 9 = 2 x = … [1] (b) 2 log x - log 4 = log 9 x = … [2]

3 marks

Mark scheme: 13(a) 3 1 13(b) 6 2 M1 for any correct use of  a  loga – log b = log   or  b  loga + log b = log (a × b) or nloga = logan

This question in 0607/23 May/June 2020

13 (a) Find log 3 . 9 … [1] (b) Solve log x + 2 log 5 = log 15 . … [2] Question 14 is printed on the next page.

3 marks

Mark scheme: 13(a) –2 1 13(b) 15 3 2 M1 for one correct use of alogb = log ba or or 0.6 25 5 b or loga – logb = log a or loga + log b = log(ab)

This question in 0607/22 Oct/Nov 2020

8 Find the value of 1 -3 (a) , b 2 l … [1] (b) log 5 125 . … [1]

2 marks

Mark scheme: 8(a) 8 cao 1 8(b) 3 cao 1

This question in 0607/23 Oct/Nov 2020

15 log x = 2 log 3 - 5 log 2 Find the value of x. x = … [2]

2 marks

Mark scheme: 15 9 2 M1 for correct use of nlogx = logxn or correct p 32 use of log p − log q = log q

This question in 0607/23 Oct/Nov 2020

20 2 log p = 3 log x - log y Find p in terms of x and y. p = … [3]

3 marks

Mark scheme: 20 3 M1 for log p 2 or log x 3 3x oe final answer y M1 for correct use of u log u − log v = log v

This question in 0607/23 May/June 2021

14 Solve. (a) log 3 x = 4 x = … [1] (b) 2 log x - 3 log 2 = log 50 x = … [3]

4 marks

Mark scheme: 14(a) 81 1 14(b) 20 3 M1 for one correct use of alog x = log xa M1 for one correct use of log a + log b = log ab a or log a – log b = log b

This question in 0607/21 Oct/Nov 2021

19 log 48 + log 18 - 2 log 24 = logt Find the value of t. t = … [3]

3 marks

Mark scheme: 19 1 3 3 M1 for correct use of log p ± log q 1.5 or 12 or 2 M1 for correct use of n log p

This question in 0607/22 Oct/Nov 2021

16 Solve. 2 log 3 - log 2 = logp p = … [2]

2 marks

Mark scheme: 16 9 2 M1 for correct use of one rule of logs 4.5 or oe 2 9 2 E.g. log  log4.5 , or 2log3  log3 2

This question in 0607/21 May/June 2022

16 Solve. 2 log x = 1 + log 9 - log 8 + 2 log 3 x = … [3] Question 17 is printed on the next page.

3 marks

Mark scheme: 16 5 3 B1 for 1  log10 M1 for one correct use of log laws eg log a  log b  log ab log a b  b log a

This question in 0607/22 May/June 2022

13 Solve. log 2x = 5 x = … [2]

2 marks

Mark scheme: 13 50000 or 5  10 4 2 B1 for 2 x = 105

This question in 0607/21 Oct/Nov 2022

14 4 log y + 3 log x = 2 Find y in terms of x. … [3]

3 marks

Mark scheme: 14 100 3 M1 for one correct use of nloga = logan y = [  ] 4 3 or log(a × b) = loga + logb x  a  or log   = loga – logb  b  B1 for 100

This question in 0607/22 Oct/Nov 2022

15 log y = log h + log p - log x Find y in terms of h, p and x. y = … [1] Questions 16 and 17 are printed on the next page.

1 marks

Mark scheme: 15 hp 1 final answer x

This question in 0607/23 Oct/Nov 2022

15 (a) Write down the value of log 10 ( 0 .01 ) . … [1] (b) Find the value of 2 log 4 + log 5 - 3 log 2 . … [3]

4 marks

Mark scheme: 15(a) –2 1 15(b) 1 3 B2 for log 10 OR M1 for any correct use of alogb = logba or loga + logb = logab  a  or loga – logb = log    b 

This question in 0607/22 May/June 2023

16 log 20 + logx = 2 Find the value of x. x = … [2]

2 marks

Mark scheme: 16 5 2 M1 for 2 = log100 or for log(20x) = 2

This question in 0607/21 Oct/Nov 2023

16 (a) log a 64 = 2 Write down the value of a. … [1] (b) Simplify log 3 + 3 log 2 - log 12. … [3]

4 marks

Mark scheme: 16(a) 8 1 16(b) log2 3 3 M1 for log 2 oe seen M1 for correct use of log a + log b = log ab or log a – log b = log a/b

This question in 0607/22 Oct/Nov 2023

14 Solve 2 log x - 3 log 2 + log 5 = 3 . x = … [4]

4 marks

Mark scheme: 14 40 4 M1 for one correct use of log a + log b = log ab or a log a – log b = log b M1 for one correct use of n log a = logan B1 for [log]1000

This question in 0607/23 Oct/Nov 2023

15 log p = 2 log 6 + log 5 - 2 Find the value of p. p = … [4]

4 marks

Mark scheme: 15 1.8 oe 4 B1 for 2 = log 100 oe M1 for correct use of logab = bloga  a M1 for correct use of log  = log a − log b  b  or logab = log a + logb

This question in 0607/22 Feb/March 2024

15 Simplify. 2 1 + 3 log 2 - 2 log 3 - 2 log 3 … [4] 16 Solve the equation. 4 ( cosx) 2 = 3 for 0° G x G 360°

4 marks

Mark scheme: 15 log 20 cao 4 B1 for 1  log10 M1 for one correct use of log a b  b log a oe M1 for one correct use of log a  log b  log ab

This question in 0607/21 May/June 2024

13 Find the value of 4 log 2 + 2 log 5 - log 4 . … [3] Question 14 is printed on the next page.

3 marks

Mark scheme: 13 2 3 M1 for one correct use of alog b = log ba M1 for one correct use of log a + log b = log ab a or log a – log b = log b

This question in 0607/23 May/June 2024

18 log 4 + 2 logx = 2 Find the value of x. x = … [3]

3 marks

Mark scheme: 18 5 cao 3 B1 for 100 M1 for one correct use of log rules

This question in 0607/22 Oct/Nov 2024

19 Solve. Give each answer as an exact value. (a) 2 x = 5 x = … [1] (b) 2 logy = 1 y = … [1]

2 marks

Mark scheme: 19(a) log5 1 or log 2 5 log2 19(b) 1 1 10 or 10 2

This question in 0607/23 May/June 2025