MAT1510
ASSIGNMENT 3, 2024
ASSIGNMENT 03
Due date: Tuesday, 25 June 2024
Total Marks: 100
UNIQUE ASSIGNMENT NUMBER: 394458
ONLY FOR YEAR MODULE
, ASSIGNMENT 03
1.1) The expression log3(3^(√(2x +5))/(3^(p) * (x -1)^5)) can be rewritten
as:
log3(3^(√(2x +5))) - log3(3^(p)) - log3((x -1)^5)
This can further be simplified as:
√(2x +5) - p * log3(3) - 5 * log3(x - 1)
Since log3(3) = 1, the final expression is:
√(2x +5) - p - 5log3(x - 1)
1.2) The expression 3/2 * ln((x^2+1)/((x+1)(x-1))) can be rewritten as a
single logarithm:
ln((x^2+1)/(x+1)(x-1))^(3/2)
The final expression is:
ln((x^2+1)/(x+1)(x-1))^(3/2)
ASSIGNMENT 3, 2024
ASSIGNMENT 03
Due date: Tuesday, 25 June 2024
Total Marks: 100
UNIQUE ASSIGNMENT NUMBER: 394458
ONLY FOR YEAR MODULE
, ASSIGNMENT 03
1.1) The expression log3(3^(√(2x +5))/(3^(p) * (x -1)^5)) can be rewritten
as:
log3(3^(√(2x +5))) - log3(3^(p)) - log3((x -1)^5)
This can further be simplified as:
√(2x +5) - p * log3(3) - 5 * log3(x - 1)
Since log3(3) = 1, the final expression is:
√(2x +5) - p - 5log3(x - 1)
1.2) The expression 3/2 * ln((x^2+1)/((x+1)(x-1))) can be rewritten as a
single logarithm:
ln((x^2+1)/(x+1)(x-1))^(3/2)
The final expression is:
ln((x^2+1)/(x+1)(x-1))^(3/2)
