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**Find the value of y such that**

log2 y= –3 Find the positive value of x such that logx 64 = 2

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Logs

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**We can simplify logs in the same way we simplify indices**

loga (xy) = logax + logay loga x = logax – logay y loga1/x = -loga x loga xn = nlogax logaa = 1 and loga1 = 0

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**Example Write as a single log log36 + log37 2log53 + 3log52**

Note : like indices, they must have the same base!

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Solving We can solve exponential equations by using logs Solve, 3x = 20

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Example 1 Solve 7x+1 = 3x+2

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Example 2 Solve 52x + 7(5x) – 30 = 0

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Example 3 Solve the equation log3(5x-1) - log3(x+1) = 1

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May 2007 qu 6 (a) Find, to 3 significant figures, the value of x for which 8x = 0.8. (2) (b) Solve the equation 2 log3 x – log3 7x = 1 (4)

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Jan 08 qu 5 Given that a and b are positive constants, solve the simultaneous equations a = 3b, log3a + log3b = 2. Give your answers as exact numbers. (6)

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