Powers 3

2 to the power of n divided by 4 to the power of -3 equal 4. What is the vaule of n?

Result

n =  0.031

Solution:

2n/4−3=4 n/4−3⋅ ln⁡(2)=ln⁡(4)  n=ln⁡(4)ln⁡(2)⋅ 43=132≐0.0313≐0.0312^{ n/ 4^{ -3 } }=4 \ \\ n/4^{ -3 } \cdot \ \ln (2)=\ln(4) \ \\ \ \\ n=\dfrac{ \ln(4) }{ \ln(2) \cdot \ 4^3 }=\dfrac{ 1 }{ 32 } \doteq 0.0313 \doteq 0.031

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