math

Calculate without using tables or calculators log 450 and log 324 given log 2 =0.3010 and log 3 =0.4771

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  1. I will do the second one
    324 = 4(81)
    = 2^2 x 3^4

    log324 = log(2^2 x 3^4)
    = log 2^2 + log 3^4
    = 2log2 + 4log3
    = 2(.3010) + 4(.4771)
    = .6020 + 1.9084
    = 2.5104

    log(450) = log(10x45)
    = log(10x9x5)
    = log10 + log 3^2 + log5 ---> need log5

    other combinations:
    450 = 5^2 x 9x2 = 5^2 x 3^2 x 2 --- still need log 5

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  2. log 450= log9 × log50
    log3^2 × log 100÷2
    Log100=2 So it's 2log3 × log 100÷2
    2 (0.4771) × 2 - 0.3010
    0.9542 + 1.699
    2.6532

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