Logarithms and exponential functions: check 1
Difficulty: ★★☆Maths4U Original · Short practice
Let a=\(3\), \(p = 2187\), \(q = 81\). Work exactly, using index laws.
Find logₐ p.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Logarithms and exponential functions: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
Let a=\(4\), \(p = 64\), \(q = 4\). Work exactly, using index laws.
Find logₐ p.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Logarithms and exponential functions: check 2
Difficulty: ★★☆Maths4U Original · Short practice
Let a=\(4\), \(p = 64\), \(q = 4\). Work exactly, using index laws.
Find logₐ(pq).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Logarithms and exponential functions: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
Let a=\(2\), \(p = 16\), \(q = 4\). Work exactly, using index laws.
Find logₐ(pq).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Logarithms and exponential functions: check 3
Difficulty: ★★☆Maths4U Original · Short practice
Let a=\(e\), \(p = e^{4}\), \(q = e^{2}\). Work exactly, using index laws.
Find logₐ(p/q).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Logarithms and exponential functions: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
Let a=\(e\), \(p = e^{7}\), \(q = e\). Work exactly, using index laws.
Find logₐ(p/q).
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Logarithms and exponential functions: check 4
Difficulty: ★★☆Maths4U Original · Short practice
\(f{\left(x \right)} = 2 \log{\left(3 x - 69 \right)} + 4\), with a=3, h=23, b=4.
Find the gradient where a(x−h)=1.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.
Logarithms and exponential functions: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
\(f{\left(x \right)} = 3 \log{\left(4 x - 96 \right)} + 5\), with a=4, h=24, b=5.
Find the gradient where a(x−h)=1.
Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.