10 questions🇬🇧English
📈 Laws of Logarithms – A-level
Maths · A-level — practises the log laws, ln and e, and solving exponential equations
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Questions
Which logarithmic statement is equivalent to 2⁵ = 32?
log₃₂ 2 = 5
log₂ 5 = 32
log₂ 32 = 5
log₅ 32 = 2
20s
Write log₃ 5 + log₃ 4 as a single logarithm:
log₃ 1.25
log₉ 20
log₃ 9
log₃ 20
20s
Solve ln(x + 1) = 2. What is the exact value of x?
x = e² + 1
x = 2e − 1
x = ln 2 − 1
x = e² − 1
20s
Which expression gives the exact solution of 3ˣ = 20?
x = ln(20 ÷ 3)
x = 20 ÷ ln 3
x = ln 3 ÷ ln 20
x = ln 20 ÷ ln 3
30s
Simplify e^(3 ln 2):
6
3e²
9
8
30s
Write 2 log 6 − log 4 as a single logarithm:
log 8
log 32
log 3
log 9
30s
If y = axⁿ, a graph of log y against log x is a straight line. What is its gradient?
a
log a
log n
n
30s
For y = kbˣ, the graph of log₁₀ y against x is a line with gradient 0.3 and intercept 2. What is k?
100
e²
2
20
30s
Solve ln x + ln(x + 2) = ln 8:
x = 2 or x = −4
x = 4 only
x = 2 only
x = 3 only
60s
Solve 2²ˣ − 5 × 2ˣ + 4 = 0:
x = 0 or x = 2
x = 2 only
x = 1 or x = 4
x = 1 or x = 2
60s