CLASS 10 · LEARNING KNOWLEDGE
Logarithms and growth duration
How it works
A logarithm answers the question about the exponent. In growth models, it can be used to calculate the time. Base and argument must satisfy the domain conditions.
Note
log_b(a)=x ⇔ b^x=a; t=ln(N/N₀)/ln(q), q>0 and q≠1.
log_b(a)=x ⇔ b^x=a; t=ln(N/N₀)/ln(q), q>0 and q≠1.
An example
Calculate the logarithm base 2 of 16. Give only the requested number.
The exponent n is sought with 2^n=16. Since 2^4=16, the logarithm is 4. Result: 4.
Try it yourself now
50 Exercises · three difficulty levels · selection and number input
To the learning unit →Own explanation and own practice exercises by AmyMath. Subject reference framework: KMK Educational Standards Mathematics ESA/MSA. The topic assignment may vary by federal state.