Laws of logarithms and equations
See the product and power laws, solve a logarithmic equation, and straighten data with logarithms.
- سوريا: الصف ١٢
- فلسطين: الصف ١٠
- إيران: الصف ١١
- أفغانستان: الصف ١١
- أوكرانيا: الصف ١١
- روسيا: الصف ١٠
- ألمانيا: الصف ١٠
- فرنسا: الصف ١٢
- بريطانيا: السنة ١٢
لم يُترجَم هذا المختبر إلى هذه اللغة بعد.
الدليل
A logarithm turns multiplying into adding: log₂(٨×٤) = log₂٨ + log₂٤. A power comes down as a multiplier: log₂(١٦٢) = ٢×log₂١٦. Change of base: log of x to base b equals log x ÷ log b, so a calculator's base 10 will do.
To solve log₂(x + ٣) = ٤, write it as a power: x + ٣ = ٢٤. Careful: do not forget to take 3 away from 16.
If y = a×bx, taking logs gives log y = log a + x×log b. So log y against x is a straight line: its gradient is log b and its height at x = 0 is log a.
Common slips: adding the numbers instead of the logs; adding instead of multiplying by the power; forgetting to move the 3 in the equation; turning the gradient upside down.