Question

my problem is as follows: Solve:

3^x-2=9^x+4

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

Answer 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