7) $$ 4 \log _{2} a-12 \log _{2} b $$

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Calculate or simplify the expression $$ 4 \log _{2} a-12 \log _{2} b $$.
Simplify the expression by following steps:
- step0: Solution:
  $$4\log_{2}{\left(a\right)}-12\log_{2}{\left(b\right)}$$
- step1: Use the logarithm base change rule:
  $$\log_{2}{\left(a^{4}\right)}-\log_{2}{\left(b^{12}\right)}$$
- step2: Transform the expression:
  $$\log_{2}{\left(\frac{a^{4}}{b^{12}}\right)}$$
- step3: Rearrange the terms:
  $$\log_{2}{\left(\left(\frac{a}{b^{3}}\right)^{4}\right)}$$
- step4: Simplify the expression:
  $$4\log_{2}{\left(\frac{a}{b^{3}}\right)}$$
The simplified form of the expression $$4 \log _{2} a-12 \log _{2} b$$ is $$4\log_{2}\left(\frac{a}{b^{3}}\right)$$.
The simplified form is $$4\log_{2}\left(\frac{a}{b^{3}}\right)$$.

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