0, \ x \ne 1\\\\
\log_{x}4 = \log_{x}x^2\\\\
4 = x^2, \ x = \pm2\\\\
\boxed{x = 2}\\\\
b) \ \log_{2x+2}16x = 1, \ 2x + 2 > 0, \ 2x + 2 \ne 1\\\\
\log_{2x+2}16x = \log_{2x+2}2x+2\\\\
16x = 2x + 2, \ 14x = 2\\\\
\boxed{x =\frac{1}{7}}
" alt="a) \ \log_{x}4 = 2, \ x > 0, \ x \ne 1\\\\
\log_{x}4 = \log_{x}x^2\\\\
4 = x^2, \ x = \pm2\\\\
\boxed{x = 2}\\\\
b) \ \log_{2x+2}16x = 1, \ 2x + 2 > 0, \ 2x + 2 \ne 1\\\\
\log_{2x+2}16x = \log_{2x+2}2x+2\\\\
16x = 2x + 2, \ 14x = 2\\\\
\boxed{x =\frac{1}{7}}
" align="absmiddle" class="latex-formula">