Question 1
Solve for $x$ in the equation $3^{2x} = 5.4$.
Worked answer
🔒 Start free to see full answer
Mathematical Methods · Unit 2 · Logarithms and logarithmic functions · Logarithms and logarithmic laws
Solve equations involving indices using logarithms, with and without technology.
Practise this objective
AI-marked practice questions tied to QCAA mark schemes for this exact LO. Free to start.
Start free practicePractice questions for this objective
Full questions, answers and worked solutions unlock when you start a free practice session.
Question 2
A new internet search engine gives a ranking R to each website based on the function R = log₁₀(25h²), where h is the number of hits (visits) the website has received. If a website currently has 80 hits, determine how many additional hits are needed to increase their ranking by 2.
Worked answer
🔒 Start free to see full answer
Question 3
Solve for \(x\) in the following. \[5^{2x+1} = 78\]
Worked answer
🔒 Start free to see full answer
More in Logarithms and logarithmic laws
← Previous
Define logarithms as indices, where 𝑎𝑥 = 𝑏 is equivalent to 𝑥 = log𝑎 (𝑏), and convert between both forms.
Next →
Use logarithmic laws and definitions log𝑎 (𝑥) + log𝑎(𝑦) = log𝑎 (𝑥𝑦) log𝑎 (𝑥) − log𝑎(𝑦) = log𝑎 (𝑥 𝑦) log𝑎 (𝑥𝑛) = 𝑛 log𝑎 (𝑥) log𝑎 (𝑥) = log𝑏(𝑥) log𝑏(𝑎) log𝑎 (𝑎) = 1 log𝑎 (1) = 0