If 2^x
= 216, then x=
Answers
Answered by
3
Answer:
2*2*2*2*2*2*2*2
2^8=216
Answered by
0
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
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