Question

Which equation is equivalent to 4^x+3=64?

a) 2^x+6=2^4
b) 2^2x+6=2^6
c) 4^2x+6=4^2
d) 4^x+3=4^6

Answer 1

the answer to this is b, 2^2x+6=2^6

Answer 2

The correct option is: b)
`2^2^x^+^6=2^6`

Explanation:

The given expression is:
`4^x^+^3=64`

Factoring out 64 will give:
`64=2* 2* 2* 2* 2* 2=2^6`

Now, the given expression becomes.....

`4^x^+^3=2^6\\ \\ (2^2)^x^+^3=2^6\ \ [As,\ 4=2^2]\\ \\ 2^2^(^x^+^3^)=2^6 \ \ [using\ 'power\ to\ the\ power'\ rule]\\ \\ 2^2^x^+^6=2^6`

So, the equivalent expression is:
`2^2^x^+^6=2^6`