How do you solve these exponential functions?

Question

Can someone explain how to solve these two examples:

22)     (2/3)^x-1 = (81/16)^x+1


20)    3^-x = (1/27)^1-x

I understood this just fine until they put fractions in and they didn't seem to relate to eachother properly, if that makes any sense.

Wile E. · Accepted Answer

(2/3)^(x-1) = (81/16)^(x+1)
(x - 1)(Log 2 - Log 3) = (x + 1)(Log 81 - Log 16)
(x - 1)(0.301 - 0.4771) = (x + 1)(1.9085 - 1.2041)
(x - 1)(- 0.1761) = (x + 1)(0.7044)
- 0.1761x + 0.1761 = 0.7044x + 0.7044
0.7044x + 0.1761x = 0.1761 - 0.7044
0.8805x = - 0.5283
x = - 0.5283 / 0.8805
x = - 0.6
¯¯¯¯¯¯¯

3^(-x) = (1/27)^(1-x)
- x Log 3 = (1 - x)(Log 1 - Log 27)
- x (0.4771) = (1 - x)(0 - 1.4314)
- 0.4771x = - 1.4314 + 1.4314x
1.4314x + 0.4771x = 1.4314
1.9085x = 1.4314
x = 1.4314 / 1.9085
x = 0.75
¯¯¯¯¯¯¯

How do you solve these exponential functions?

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