Ben asked in Science & MathematicsMathematics · 1 decade ago

8 to the power of r = 16 Squared, How do you solve this?

Update:

What is R?

2 Answers

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  • np_rt
    Lv 4
    1 decade ago
    Favorite Answer

    8^r = 16^2

    (2^3)^r = (2^4)^2

    2^(3r) = 2^8

    3r = 8

    r = 8/3

    Note that you won't always be able to solve it this way to get rational numbers. Here's how you would do it in general.

    8^r = 16^2 = 256

    ln(8^r) = ln(256)

    r*ln(8) = ln(256)

    r = ln(256)/ln(8)

    This is usually where it ends but in our case it can be simplified.

    r = ln(2^8)/ln(2^3)

    = 8*ln(2)/[3*ln(2)]

    = 8/3

  • Como
    Lv 7
    1 decade ago

    8^r = 256

    Take log base 2 of both sides:-

    r log 8 = log 256

    3 r = 8

    r = 8 / 3

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