Investigating Logarithms

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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 ...read more.

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 ...read more.

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 ...read more.

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