### Home > A2C > Chapter 3 > Lesson 3.2.2 > Problem3-110

3-110.

Solve the following equations for x, if possible. Some you can solve exactly, others approximately. If a solution is not possible, explain how you know.

1. $1^{x} = 5$

$1^{1} = 1\\1^{3} = 1\\1^{2} = 1\\1^{4} = 1$

No solution. Explain why.

1. $\sqrt { 27 ^ { x } } = 81$

Rewrite in exponential form.

$81$ and $27$ can both be rewritten as powers of $3$.

Simplify the exponents and solve for x.

$x=\frac{8}{3}=2.\overline{6}$

1. $2^{x} = 9$
1. $25^{(x+1)} = 125^{x}$
1. $8^{x} = 2^{5} · 4^{4}$