Logarithmic equations and domain checks: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(\log_{4}(x - 21)+\log_{4}(x - 18)=\log_{4}(10)\). Here \(\displaystyle h=21\).
Find the valid solution x.
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.
Logarithmic equations and domain checks: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(\log_{2}(x - 22)+\log_{2}(x - 21)=\log_{2}(12)\). Here \(\displaystyle h=22\).
Find the valid solution x.
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.
Logarithmic equations and domain checks: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(\log_{2}(x - 22)+\log_{2}(x - 21)=\log_{2}(12)\). Here \(\displaystyle h=22\).
Find the rejected algebraic root.
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.
Logarithmic equations and domain checks: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(\log_{3}(x - 23)+\log_{3}(x - 21)=\log_{3}(24)\). Here \(\displaystyle h=23\).
Find the rejected algebraic root.
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.
Logarithmic equations and domain checks: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(\log_{3}(x - 23)+\log_{3}(x - 21)=\log_{3}(24)\). Here \(\displaystyle h=23\).
Find x−h at the valid solution.
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.
Logarithmic equations and domain checks: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(\log_{4}(x - 24)+\log_{4}(x - 21)=\log_{4}(40)\). Here \(\displaystyle h=24\).
Find x−h at the valid solution.
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.
Logarithmic equations and domain checks: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(\log_{4}(x - 24)+\log_{4}(x - 21)=\log_{4}(40)\). Here \(\displaystyle h=24\).
Find the product of the two logarithm arguments at the valid solution.
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.
Logarithmic equations and domain checks: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Solve \(\log_{2}(x - 25)+\log_{2}(x - 24)=\log_{2}(6)\). Here \(\displaystyle h=25\).
Find the product of the two logarithm arguments at the valid solution.
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.