CPM Homework Help : A2C Problem 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.

$1^{x} = 5$
Hint (a):
$1^{1} = 1\\1^{3} = 1\\1^{2} = 1\\1^{4} = 1$
Answer (a):
No solution. Explain why.

$\sqrt { 27 ^ { x } } = 81$
Hint (b):
Rewrite in exponential form.
Hint 2 (b):
$81$ and $27$ can both be rewritten as powers of $3$ .
More Help (b):
Simplify the exponents and solve for x.
Answer (b):
$x=\frac{8}{3}=2.\overline{6}$
Remember to check your answer.

$2^{x} = 9$
Hint (c):
Create and complete a guess and check table to help you solve the problem.

$25^{(x+1)} = 125^{x}$
Hint (d):
See part (b).

$8^{x} = 2^{5} · 4^{4}$
Hint (e):
See part (b).