## What number goes in the box? 2 ^ ( ) = (2^7 ÷ 2^9)^3

Question

What number goes in the box?
2 ^ ( ) = (2^7 ÷ 2^9)^3

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1 year 2021-07-31T03:45:02+00:00 1 Answers 5 views 0

$$x=-6$$
$$(\frac{2^{7}}{2^{9}})^{3} \\(\frac{128}{512})^{3} \\(\frac{1}{4})^{3}\\(\frac{1}{4})*(\frac{1}{4})*(\frac{1}{4})\\\frac{1*1*1}{4*4*4} \\\frac{1^{3} }{4^{3} } \\\frac{1}{64} \\2^{x}=\frac{1}{64}\\log 2^x=log\frac{1}{64}\\x*(log(2))=log\frac{1}{64}\\x=\frac{log\frac{1}{64}}{log(2)} \\x=-6$$