\log _2\left(x+1\right)-4\log _4\left(x^2\right)+3\log _2\left(x\right)

asked by guest
on Oct 28, 2024 at 12:15 am



You asked:

Evaluate the expression: \(\log_{2}\left( x + 1 - 4 \cdot \log_{4}\left( {x}^{2} + 3 \cdot \log_{2}\left( x \right) \right) \right)\)

MathBot Answer:

Evaluated



\(\displaystyle \log_{2}\left( x + 1 - 4 \cdot \log_{4}\left( {x}^{2} + 3 \cdot \log_{2}\left( x \right) \right) \right) = \frac{\log{\left(x - \frac{4 \log{\left(x^{2} + \frac{3 \log{\left(x \right)}}{\log{\left(2 \right)}} \right)}}{\log{\left(4 \right)}} + 1 \right)}}{\log{\left(2 \right)}} \)

Factored

\[\log_{2}\left( x + 1 - 4 \cdot \log_{4}\left( {x}^{2} + 3 \cdot \log_{2}\left( x \right) \right) \right) = \frac{\log{\left(x - \frac{2 \log{\left(x^{2} + \frac{3 \log{\left(x \right)}}{\log{\left(2 \right)}} \right)}}{\log{\left(2 \right)}} + 1 \right)}}{\log{\left(2 \right)}}\]

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