Question

If 2^x

= 216, then x=​

Answer 1

Answer:

2*2*2*2*2*2*2*2

2^8=216

Answer 2

Answer:

x=3

Step-by-step explanation:

Noting that

log2x(216)=ln(216)ln(2x)

log2x⁡(216)=ln⁡(216)ln⁡(2x)

we can say

log2x(216)ln(216)ln(2x)ln(216)eln(216)eln(216)216=x=x=xln(2x)=exln(2x)=eln((2x)x)=(2x)x

log2x⁡(216)=xln⁡(216)ln⁡(2x)=xln⁡(216)=xln⁡(2x)eln⁡(216)=exln⁡(2x)eln⁡(216)=eln⁡((2x)x)216=(2x)x

We can then note that 216=63216=63 and so

63(2×3)3=(2x)x=(2x)x

63=(2x)x(2×3)3=(2x)x

It is then trivial to see that x=3x=3

We could also calculate this last step by noting that the exponent must be half the base.

We can then brute force this with integers:

Starting with an exponent of 11, we have

214263=2=16=216

21=242=1663=216

And so our exponent, and thus x, must be 3