Question

Solve this equation 2^x-2=8^4

Answer 1

`\huge\boxed{\sf x = 14}`

Explanation:

Given equation:

`2^(x-2)=8^4`

We can write 8 as 2³ because 8 = 2 × 2 × 2

So,

`2^(x-2)=(2^3)^4\\\\2^(x-2)=2^(12)`

By comparing both sides, we get:

x - 2 = 12

• Add 2 to both sides

x = 12 + 2

x = 14

`\rule[225]{225}{2}`

Answer 2

x = 14

Explanation:

2^(x-2)=8^4

Rewriting 8 as 2^3

2^(x-2)=2^3^4

We know that a power to a power is multiply

2^(x-2)=2^12

The bases are the same so the exponents are the same

x-2 =12

x = 14