Investigating Logarithms

Extracts from this essay...

Introduction

Investigating Logarithms log2 + log3 0.7782 log6 0.7782 log3 + log7 1.322 log21 1.322 log4 + log 20 1.903 log80 1.903 log0.2 + log11 0.3424 log2.2 0.3424 log0.3 + log 0.4 -0.9208 log0.12 -0.9208 This table to the left clearly shows that the log of 2 numbers added together will equal the log of the number multiplied. The table below clearly shows that log (?) + log (y) will equal log (?y). Let log x = a, let log y = b. Therefore 10a = x and 10b = y, these two equations can then be simplified to 10(a+b) =x*y. it is then possible to convert this back to log (xy) = a + b. log5 + log4 log20 1.301 log3 + log2 log6 0.7782 log4 + log8 log32 1.505 log6 + log3 log18 1.255 log3 + log26 log78

Middle

- log () will equal log (). Let log x = a, let log y = b. Therefore 10a = x and 10b = y, these two equations can be converted into 10(a - b) = x/y. Finally, this equation can then be converted back into log x - log y = log (x/y). log6 - log2 log3 0.4771 log18 - log3 log6 0.7782 log 16 - log 2 log8 0.9031 log50 - log5 log10 1 log25 - log5 log5 0.6989 log32 - log8 log4 0.6021 4 log2 1.204 log24 1.204 5 log6 3.891 log65 3.891 1/2 log4 0.3011 log41/2 0.3011 2/5 log7 0.3380 log72/5 0.3380 -3 log5 -2.097 log5-3 -2.097 3 log6 log63 2.3345 4 log2 log24 1.2041 2 log8 log82 1.8062 5 log7 log75 4.2255 7 log3 log37 3.3398 6 log4 log46 3.6124 The table located to the

Conclusion

Let's investigate the function y = log x When x = 1, y = log1, therefore, y = 0 Therefore when y = 0, x will equal 1. On a graph this would mean that the curve would cut the x axis at 1. In this function x cannot equal zero or less than zero, this means that the restricted domain of the function will be {x: x>1}. x 0.000001 0.00001 0.0001 0.001 0.01 0.1 1 y = log x -6 -5 -4 -3 -2 -1 0 The table above displays that as x is multiplied by ten, the y value increases by 1. x 1 2 3 4 5 6 7 8 9 10 y = log x 0 0.3010 0.4771 0.6021 0.6989 0.7782 0.8451 0.9010 0.9542 1 The graph below demonstrates the curve of the function y = log x ?? ?? ?? ?? Jeremiah Joseph Jeremiah Joseph Maths Internal Assessment Mr. Filander

The above preview is unformatted text

Found what you're looking for?

  • Start learning 29% faster today
  • Over 150,000 essays available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Over 180,000 student essays
  • Every subject and level covered
  • Thousands of essays marked by teachers
  • Over 180,000 essays
    written by students
  • Annotated by
    experienced teachers
  • Ideas and feedback to write
    your own great essays

Marked by a teacher

This essay has been marked by one of our great teachers. You can read the full teachers notes when you download the essay.

Peer reviewed

This essay has been reviewed by one of our specialist student essay reviewing squad. Read the full review on the essay page.

Peer reviewed

This essay has been reviewed by one of our specialist student essay reviewing squad. Read the full review under the essay preview on this page.