Aplications of logarithms

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Applications of 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.

Have a look at the following worked example. 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.

After 14 days the power output has fallen to 56 watts. Calculate the value of k to three decimal places.

The satellite cannot function properly if the power output falls below 5 watts. How many days will the satellite function properly?

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.)

Here's another example for you to consider. Given the straight line graph below, which has equation of the form , you are usually asked to determine the values of and . We'll take you through the calculation step by step.

Line intersecting y axis at 6

There are two methods you could use.

The first takes as a starting point the fact that the line is a straight line, so its equation takes the form

and c = 6

so and n = 3 and (or 1000000)

The other method you could use starts with and takes of both sides.

Therefore

compare this with the equation of the line

y = mx + c where and c = 6

so n = 3 and

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