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C2: Change of Base of Logarithms

C2: Change of Base of Logarithms. Learning Objective: to understand that the base of a logarithm may need changing to be able to solve an equation. Changing the base of a logarithm. So:. 5 x = 8. So:. Suppose we wish to calculate the value of log 5 8.

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C2: Change of Base of Logarithms

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  1. C2: Change of Base of Logarithms Learning Objective: to understand that the base of a logarithm may need changing to be able to solve an equation

  2. Changing the base of a logarithm So: 5x = 8 So: Suppose we wish to calculate the value of log5 8. We can’t calculate this directly using a calculator because it only find logs to the base 10 or the base e. We can change the base of the logarithm as follows: Let x = log5 8 Taking the log to the base 10 of both sides: log 5x = log 8 x log 5 = log 8 1.29 (to 3 s.f.)

  3. Changing the base of a logarithm So: In general, to find logab: Let x = loga b, so we can write ax = b Taking the log to the base c of both sides gives: logcax = logcb xlogca = logcb

  4. Example : We can use the change of base of logarithms to solve equations. For example: Find, to 3 significant figures log8 11. We can solve this by changing to base 10: log8 11 = log10 11 / log10 8 Using a calculator: x = 1.15 (to 3 s.f.)

  5. Task 1 : Find to 3 d.p. • log7 120 • log3 45 • log2 19 • log11 3 • log6 4 Solve 8x = 14, 9x = 99, 12x = 6

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