Indices, Surds and Logarithms Archives - SPM Additional Mathematics

4.6.2 Indices and Logarithms, SPM Practice (Long Questions)

January 21, 2022May 13, 2020 by

4.6.2 Indices and Logarithms, SPM Practice (Long Questions) Question 3: Given that p = 3r and q = 3t, express the following in terms of r and/ or t. (a) (a) log 3 p q 2 27 , (b) log9p – log27 q. Solution: (a) Given p = 3r, log3 p = r q= 3t, log3 q =t … Read more

4.6.1 Indices and Logarithms, SPM Practice (Long Questions)

January 21, 2022May 12, 2020 by

4.6.1 Indices and Logarithms, SPM Practice (Long Questions) Question 1: (a) Find the value of i. 2 log2 12 + 3 log25 – log2 15 – log2 150. ii. log832 (b) Shows that 5n + 5n + 1 + 5n + 2 can be divided by 31 for all the values of n … Read more

4.5.4 Indices and Logarithms, Short Questions (Question 11 – 13)

January 21, 2022May 10, 2020 by

Question 11 Given that 2 log2 (x – y) = 3 + log2x + log2 y. Prove that x2 + y2– 10xy = 0. Solution: 2 log2 (x – y) = 3 + log2x + log2 y log2 (x– y)2 = log2 8 + log2 x + log2y log2 (x– y)2 = log2 8xy (x … Read more

4.5.3 Indices and Logarithms, Short Questions (Question 8 – 10)

January 21, 2022May 9, 2020 by

Question 8 Solve the equation, log 9 ( x − 2 ) = log 3 2 Solution: log 9 ( x − 2 ) = log 3 2 log a b = log c b log c a ⇒ log 3 ( x − 2 ) log 3 9 = log 3 2 log 3 … Read more

4.5.2 Indices and Logarithms, Short Questions (Question 5 – 7)

January 21, 2022May 7, 2020 by

Question 5 Solve the equation, log 2 4 x = 1 − log 4 x Solution: log 2 4 x = 1 − log 4 x log 2 4 x = 1 − log 2 x log 2 4 log 2 4 x = 1 − log 2 x 2 2 log 2 4 x … Read more

4.5.1 Indices and Logarithms, Short Questions (Question 1 – 4)

January 21, 2022May 5, 2020 by

Question 1 Solve the equation, log3 [log2(2x – 1)] = 2 Solution: log3 [log2 (2x – 1)] = 2 ← (if log a N = x, N = ax) log2 (2x – 1) = 32 log2 (2x – 1) = 9 2x – 1 = 29 x = 256.5 Question 2 Solve the equation, l o g … Read more

4.4.4 Logarithms Equation – Example 4 & 5

January 21, 2022May 3, 2020 by

Example 4Solve the following equation :(a) log 9 ( x − 2 ) = log 3 2 (b) log 4 x = 3 2 log 2 3 Example 5Solve the following :(a) log 4 x = 25 log x 4 (b) log 2 5 x + log 4 16 x = 6

4.4.2 Logarithms Equation – Example 2 & 3

January 21, 2022May 1, 2020 by

Example 2Solve the following equation:(a) log y 81 − 3 = log y 3 (b) 2 log 2 x − log 2 ( x 2 − 1 ) − 4 = 0 Example 3Sole the following equation:(a) log 3 [ log 2 ( 2 x − 1 ) ] = 2 (b) log 16 [ … Read more

4.4 Equations Involving Logarithms

January 21, 2022April 30, 2020 by

METHOD:For two logarithms of the same base, if log a m = log a n , then m = n . Convert to index form, if log a m = n , then m = an. Example 1Solve the following equation:(a) log 3 2 + log 3 ( x + 5 ) = log 3 … Read more

4.3.5 Example 5 (Unequal Base – put log both side)

January 21, 2022April 29, 2020 by

Example 5Solve each of the following.(a) 3 x + 1 = 7 (b) 2 ( 3 x ) = 5 (c) 2 x .3 x = 9 x − 4 (d) 5 x − 1 .3 x + 2 = 10