151,000 views
28 votes
28 votes
Find the value of x in 4^x+64^x= 272

User Ziyao  Li
by
3.0k points

1 Answer

11 votes
11 votes

Answer:

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

User Akisha
by
2.6k points