Exponential equations reducible to quadratics · 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

Exponential equations via substitution — objective 1

Maths4U Original · Short practice

Solve \(2^{2x}-34(2^x)+64=0\).

Find the smaller 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

Exponential equations via substitution — objective 1

Maths4U Original · Short practice

Solve \(3^{2x}-252(3^x)+2187=0\).

Find the smaller 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

Exponential equations via substitution — objective 2

Maths4U Original · Short practice

Solve \(3^{2x}-252(3^x)+2187=0\).

Find the larger 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

Exponential equations via substitution — objective 2

Maths4U Original · Short practice

Solve \(4^{2x}-16448(4^x)+1048576=0\).

Find the larger 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.

Apply

Exponential equations via substitution — objective 3

Maths4U Original · Short practice

Solve \(4^{2x}-16448(4^x)+1048576=0\).

Find the product of the two x-solutions.

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

Exponential equations via substitution — objective 3

Maths4U Original · Short practice

Solve \(2^{2x}-18(2^x)+32=0\).

Find the product of the two x-solutions.

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

Exponential equations via substitution — objective 4

Maths4U Original · Short practice

Solve \(2^{2x}-18(2^x)+32=0\).

Find the difference between the larger and smaller x-solutions.

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

Exponential equations via substitution — objective 4

Maths4U Original · Short practice

Solve \(3^{2x}-738(3^x)+6561=0\).

Find the difference between the larger and smaller x-solutions.

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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