How to Solve Exponential Equations?

[froilan041]

Can anyone show me how to solve the following equations:

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

3^(x+1)+3^(x)=36
I would greatly appreciate your assistance.

 

[rock.freak667]

2^x-1=2^x*2^-1.

It should be a bit easier now.

 

[SnipedYou]

Here is a general way to solve things like this
1. $$2^{x-1}-2^{x} = 2^{-3}$$
Now factor out a $$2^{x-1}$$
$$2^{x-1}(1 - 2) = 2^{3} \rightarrow 2^{x - 1} = -\frac{1}{8}$$
You can take the logarithm at this point or you could notice that $$-\frac{1}{8}$$ is out of the range of $$2^{x}$$

Similar approach
2. $$3^{x+1} + 3^{x} = 36 \rightarrow<br /> 3^{x}(3 + 1) = 36 \rightarrow<br /> 3^{x} = 9 \rightarrow<br /> x = 2$$