logarithim

my problem is as follows: Solve:

3^x-2=9^x+4

do I "log" both sides or "ln" both nor either?

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  1. remember that 9^x = (3^2)^x = 3^(2x)
    so, setting everything to base 3, you have

    3^(x-2) = 3^(2(x+4))

    now take logs to base 3 on both sides (meaning: if the numbers are equal, then the powers are equal), to get

    x-2 = 2(x+4)
    x = -10

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