\log _2\left(x+1\right)-4\log _4\left(x^2\right)+3\log _2\left(x\right)
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
\[\log_{2}\left( x + 1 - 4 \cdot \log_{4}\left( {x}^{2} + 3 \cdot \log_{2}\left( x \right) \right) \right) = \frac{\log{\left(x - \frac{2 \log{\left(x^{2} + \frac{3 \log{\left(x \right)}}{\log{\left(2 \right)}} \right)}}{\log{\left(2 \right)}} + 1 \right)}}{\log{\left(2 \right)}}\]