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Math Help - Exponential and Log problems

  1. #1
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    Exponential and Log problems

    1. if 4e^(2-x)=128, find x, giving this answer in exact form.

    2. solve the equation loge(3x+5)-loge(2)=2 for x.

    3. solve for x given that log2(x)=y+log2(z). State restrictions to parameters.

    4. If loge(x)=a, then e^2a+3e^a-2e^-a is equal to?
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  2. #2
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    1. First divide both sides by 4 to give e^(2-x) = 32. Then take logarithms.

    2. Use the rule log(a) - log(b) = log(a/b) to simplify the left hand side, before exponentiating both sides.

    3. Use the fact that if log_a(m) = n then m = a^n to solve for x. What restrictions do you know of when dealing with logarithms and exponentials?

    4. Hints: e^(2a) = (e^a)^2, e^(-a) = 1/e^a.
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