Exponential Equations & Logs — practice questions

Algebraic Methods · Part 3 of 4

6 exam-style questions with model answers, plus 8 quick multi-choice questions — every question on this part of the standard, grouped by the 2 pages of notes they come from.

Write a full answer before you reveal the model one. That comparison is where the learning happens.

Logarithms and the log laws

Read the notes →

AchievedShow

Evaluate $\log_3 81$ and write $\log_2 32 = 5$ in index form.

MeritShow

Express $2\log x - 3\log y + \log 5$ as a single logarithm.

ExcellenceShow

Solve $\log_2(x + 6) - \log_2(x - 1) = 2$ , and explain why an apparent solution must sometimes be rejected in equations of this type.

Solving exponential equations

Read the notes →

AchievedShow

Solve $2^{x} = 64$ and $5^{x} = 90$ , giving the second answer to 3 significant figures.

MeritShow

Solve $4 \times 3^{2x-1} = 100$ , giving your answer to 3 significant figures.

ExcellenceShow

Solve $4^{x} - 9\left(2^{x}\right) + 8 = 0$ for $x$ , giving exact answers where possible.

Back to the Algebraic Methods notes →

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Exponential Equations & Logs — practice questions

Algebraic Methods · Part 3 of 4

6 exam-style questions with model answers, plus 8 quick multi-choice questions — every question on this part of the standard, grouped by the 2 pages of notes they come from.

Write a full answer before you reveal the model one. That comparison is where the learning happens.

Logarithms and the log laws

Read the notes →

AchievedShow

Evaluate $\log_3 81$ and write $\log_2 32 = 5$ in index form.

MeritShow

Express $2\log x - 3\log y + \log 5$ as a single logarithm.

ExcellenceShow

Solve $\log_2(x + 6) - \log_2(x - 1) = 2$ , and explain why an apparent solution must sometimes be rejected in equations of this type.

Solving exponential equations

Read the notes →

AchievedShow

Solve $2^{x} = 64$ and $5^{x} = 90$ , giving the second answer to 3 significant figures.

MeritShow

Solve $4 \times 3^{2x-1} = 100$ , giving your answer to 3 significant figures.

ExcellenceShow

Solve $4^{x} - 9\left(2^{x}\right) + 8 = 0$ for $x$ , giving exact answers where possible.

Back to the Algebraic Methods notes →