### Home > INT3 > Chapter 5 > Lesson 5.1.1 > Problem5-11

5-11.

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

1. $1^x=5$

$1^1=1$

$1^2=1$

$1^3=1$

$1^4=1$

No solution. Explain why.

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

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

Square root is the same as an exponent of $^{\frac{1}{2}}$. Simplify the exponents and solve for $x$.

$x = \frac{8}{3}$

1. $2^x=9$

You will need to approximate a solution.

1. $25^{(x+1)}=125^x$

Rewrite the equation using powers of $5$.

1. $8^x=2^5·4^4$

Rewrite the equation using powers of $2$.