CPM Homework Help : INT3 Problem 5-11

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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.

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

$\sqrt { 27 ^ { x } } = 81$
Hint (b):
$81$ and $27$ can both be rewritten as powers of $3$ .
More Help (b):
Square root is the same as an exponent of $^{\frac{1}{2}}$ . Simplify the exponents and solve for $x$ .
Answer (b):
$x = \frac{8}{3}$

$2^x=9$
Hint (c):
You will need to approximate a solution.

$25^{(x+1)}=125^x$
Hint (d):
Rewrite the equation using powers of $5$ .

$8^x=2^5·4^4$
Hint (e):
Rewrite the equation using powers of $2$ .

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