Derek and Donovan were trying to solve the equation 4⁴ = 16^x . Derek had an idea.
“I know,” he said. “Isn't 16 equal to 4² ?”
“Yeah, so what?” said Donovan.
“That means that we can rewrite the equation to look like 4⁴ = (4²)^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 (2²)⁴ = (2⁴)^x?” Homework Help ✎

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

2. Use both methods to solve 4⁴ = 16 ^x .

3. Now solve 3⁵ = 9^2x .