Exponential and logarithmic functions
Types of exercises: exponential function, logarithmic function, exponential growth and decay, logarithmic scales in applications, exponential function - base, monotonicity, range, logarithmic function - base, point of the graph, zero, domain.
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For which argument does the function take this value?
f(x) = 3 · log₉ x, f(x) = 9
Compute the value of the function
f(x) = −2 · 4ˣ, f(−3) = ?
Solve the problem using the definition of a logarithm
The sound level in decibels is L = 10 · log(I/I₀), where I is the sound intensity in W/m² and I₀ = 10⁻¹² W/m². The sound level of one sound is 40 dB and of another one 20 dB. How many times greater is the intensity of the first sound than the intensity of the second one?
Find the base a
The graph of the function f(x) = logₐ x, where a > 0 and a ≠ 1, passes through the point (1/25, −2).
Give the number of bacteria
The number of bacteria in a culture doubles every 10 minutes. At first there were 100 bacteria. How many bacteria will there be after 30 minutes?
Give the range of the function f
The function f is given by the formula f(x) = (1/2)ˣ + 9.
Compute the value of the function
f(x) = 6 · log₉ x, f(81) = ?
Compute the value of the function
f(x) = 5 · 10ˣ, f(5) = ?
Solve the problem using the definition of a logarithm
The Richter magnitude of an earthquake is R = log(A/A₀), where A is the amplitude of the earthquake in centimetres and A₀ = 10⁻⁴ cm. One earthquake had magnitude 4 and another one 2. How many times greater was the amplitude of the first one than the amplitude of the second one?
Give the zero of the function f
The function f is given by the formula f(x) = log₂ x − 4.
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