Question

Find the value of x in 4^x+64^x= 272

Answer 1

1.342

Explanation:

4^x+64^x=272

4^x+(4^3)^x=272

4^3x+4^x=272

(4^x)^3+4^x=272

(4^x)^3+4^x-272=0

u^3+u-272=0 ==> substitute 4^x with u

Now, use synthetic division to find roots:

`\sqrt[3]{272}`31 | 1 0 1 -272

`\sqrt[3]{272}`1
`\sqrt[3]{272^2}` 272

1
`\sqrt[3]{272}`1
`\sqrt[3]{272^2}` 0

4^x=
`\sqrt[3]{272}`

log 4 (4^x)=log 4 (
`\sqrt[3]{272}`)=1.342