Logarithmic equations and domain checks · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Logarithmic equations and domains — objective 1

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.

Fresh review variant

Logarithmic equations and domains — objective 1

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.

Method

Logarithmic equations and domains — objective 2

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.

Fresh review variant

Logarithmic equations and domains — objective 2

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.

Apply

Logarithmic equations and domains — objective 3

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.

Fresh review variant

Logarithmic equations and domains — objective 3

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.

Check understanding

Logarithmic equations and domains — objective 4

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.

Fresh review variant

Logarithmic equations and domains — objective 4

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.

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