1.) 2^(x) = 3 ^(x-1)

2.) 3^(x+2) = 5^ ( x - 1)

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- Sep 26th 2006, 06:28 AM^_^Engineer_Adam^_^Logarithm help t-t
1.) 2^(x) = 3 ^(x-1)

2.) 3^(x+2) = 5^ ( x - 1) - Sep 26th 2006, 08:08 AMtopsquark
2^x = 3^(x+1)

Take the natural log of both sides (any base will do, actually).

ln[2^x] = ln[3^(x+1)] <--- log[a^x] = x*log(a) for all bases.

x*ln(2) = (x+1)*ln(3)

x*[ln(2) - ln(3)] = ln(3)

x = ln(3)/[ln(2) - ln(3)] = -ln(3)/[ln(3) - ln(2)]

(The last step isn't really necessary, I just find it to be a bit tidier since x is negative.)

-Dan - Sep 26th 2006, 08:11 AMtopsquark
- Sep 26th 2006, 03:47 PM^_^Engineer_Adam^_^
thanks and gudluk 2 me :D