Maths
Logarithms
The examples below illustrate the main applications of logarithms (and exponential functions) which appear in the Higher Mathematics examination.
Given any equation of the form you will either be asked to work out one of the unknowns, or to carry out a calculation involving this equation.
The power supply of a space satellite is by means of a radioisotope. The power output, in watts, is given by where is the time in days. The power output at launch is 60 watts.
First, calculate the value of to three decimal places.
substitute the values you have into the formula
simplify
use the laws of logarithms to separate
solve
k = -0.005
(or )
Secondly, work out how many days it will take for the power output to reach 5 watts.
When
The total number of days it will take for the power output to reach 5 watts will be 496. (Note, on the 497th day, the power output will have fallen below 5 watts.)
Links
Scottish Qualifications Authority Maths resources, including Past Papers, Arrangements Documents, and Marking Guidelines.
Links
A review of logarithms. Let the folk at S.O.S. Maths help you get your head around logarithms
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