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Math Help - Write the expression

  1. #1
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    Question Write the expression

    Write the expression LoGa(y+5)+2loga(x+1) as one logarithm. My answer is loga(y+2x+7), but not sure if thats right. thanks for looking.
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  2. #2
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    Hello, kwtolley!

    Write the expression \log_a(y+5) + 2\log_a(x+1) as one logarithm.

    My answer is: \log_a(y+2x+7), but not sure if thats right.

    You're expected to know the three Properties of Logarithms:
    . . [1]\;\log_b(XY) \:= \:\log_b(X) + \log_b(Y)
    . . [2]\;\log_b\left(\frac{X}{Y}\right) \:=\:\log_b(X) - \log_b(Y)
    . . [3]\;\log_b\left(X^n\right) \:= \:n\cdot\log_b(X)


    So we have: . \log_a(y+5) + 2\log_a(x+1)

    . . . . . . . . = \;\log_a(y+5) + \log_a(x+1)^2 . . . property [3]

    . . . . . . . . = \;\log_a\left[(y+5)(x+1)^2\right] . . . property [1]

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  3. #3
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    thanks

    you for checking my answer
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