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Please note, there are more questions than what I'm going to give, in total I'll be giving 3. I hope to use the information with the others.

1)

Solve the equation:

[tex]5^{1-2x} = \frac{1}{5}[/tex]

None

I was thinking that to make live easier, to put the entire fraction up to the first power. From there, I would use algebra in the sense of:

[tex]1-2x=1[/tex]

[tex]-2x=0[/tex]

To get x = 0. But, that doesn't seem to be possible, since the exponent must turn out to be negative.

2)

Solve the Equation:

[tex]8^{x^{2} - 2x}} = \frac{1}{2}[/tex]

None

For this one, I was thinking of setting the fraction equal to 1, then factoring that out to get two answers:

[tex]x^2 - 2x = 1[/tex] [tex]x^2 - 2x - 1 = 0[/tex]

But, then I'm stuck there.

3)

Solve the equation:

[tex]e^{x^2} = (e^{3x})(\frac{1}{e^2})[/tex]

None

I'm completely clueless on this one.

1)

**1. Homework Statement**Solve the equation:

[tex]5^{1-2x} = \frac{1}{5}[/tex]

**2. Homework Equations**None

**3. The Attempt at a Solution**I was thinking that to make live easier, to put the entire fraction up to the first power. From there, I would use algebra in the sense of:

[tex]1-2x=1[/tex]

[tex]-2x=0[/tex]

To get x = 0. But, that doesn't seem to be possible, since the exponent must turn out to be negative.

2)

**1. Homework Statement**Solve the Equation:

[tex]8^{x^{2} - 2x}} = \frac{1}{2}[/tex]

**2. Homework Equations**None

**3. The Attempt at a Solution**For this one, I was thinking of setting the fraction equal to 1, then factoring that out to get two answers:

[tex]x^2 - 2x = 1[/tex] [tex]x^2 - 2x - 1 = 0[/tex]

But, then I'm stuck there.

3)

**1. Homework Statement**Solve the equation:

[tex]e^{x^2} = (e^{3x})(\frac{1}{e^2})[/tex]

**2. Homework Equations**None

**3. The Attempt at a Solution**I'm completely clueless on this one.

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