Logarithms and exponentials: review: check 1
Difficulty: ★★☆Maths4U Original · Short practice
Solve \(\log_{4}(x - 21)+\log_{4}(x - 18)=\log_{4}(10)\). Here h=21.
Find the valid solution x.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Logarithms and exponentials: review: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
Solve \(\log_{2}(x - 22)+\log_{2}(x - 21)=\log_{2}(12)\). Here h=22.
Find the valid solution x.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Logarithms and exponentials: review: check 2
Difficulty: ★★☆Maths4U Original · Short practice
Solve \(\log_{2}(x - 22)+\log_{2}(x - 21)=\log_{2}(12)\). Here h=22.
Find the rejected algebraic root.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Logarithms and exponentials: review: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
Solve \(\log_{3}(x - 23)+\log_{3}(x - 21)=\log_{3}(24)\). Here h=23.
Find the rejected algebraic root.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Logarithms and exponentials: review: check 3
Difficulty: ★★☆Maths4U Original · Short practice
Solve \(3^{2x}-252(3^x)+2187=0\).
Find the product of the two x-solutions.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Logarithms and exponentials: review: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
Solve \(4^{2x}-16448(4^x)+1048576=0\).
Find the product of the two x-solutions.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Logarithms and exponentials: review: check 4
Difficulty: ★★☆Maths4U Original · Short practice
A quantity is modelled by \(Q{\left(t \right)} = 26 + 12 e^{- 4 t}\) for t≥0. Here L=26, A=12, k=4.
Find the limiting value as t increases without bound.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.
Logarithms and exponentials: review: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
A quantity is modelled by \(Q{\left(t \right)} = 27 + 14 e^{- t}\) for t≥0. Here L=27, A=14, k=1.
Find the limiting value as t increases without bound.
Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.