### Home > A2C > Chapter 3 > Lesson 3.1.2 > Problem3-30

3-30.

Derek and Donovan were trying to solve the equation $4^{4} = 16^{x}$ . Derek had an idea.
“I know,” he said. “Isn't $\mathit{16}$ equal to $\mathit{4^{2}}$?”
“Yeah, so what?” said Donovan.
“That means that we can rewrite the equation to look like $\mathit{4^{4} = \left(4^{2}\right)^{x}}$. This is much easier to solve!” replied Derek.
“Yes,” said Donovan. “That makes sense. Isn't there another way, too? Since 4 is the same as 22 and 16 is the same as 24 ,
can't we rewrite it as
$\mathit{(2^{2})^{4} = (2^{4})^x}$?”

1. What do you think of Derek's and Donovan's methods? Will they both work?

Are these methods violating any rules or properties of exponents?

2. Use both methods to solve $4^{4} = 16 ^{x}$ .

$x = 2$

3. Now solve $3^{5} = 9^{2x}$ .

$x = 1.25$