Chapter 7

$$ 4 \cdot 3^{x+2}+5 \cdot 3^{x}-7 \cdot 3^{x+1}=40 $$

$$ 16^{\frac{x+5}{x-7}}=512 \cdot 64^{\frac{x+17}{x-3}} $$

$$ 5^{|4 x-6|}=25^{3 x-4} $$

$$ \sqrt{3} \cdot\left(3^{\frac{x}{1+\sqrt{x}}}\right) \cdot\left(\frac{1}{3}\right)^{\frac{2+\sqrt{x}+x}{2(1+\sqrt{x})}}=81 $$

$$ \left(\frac{3}{5}\right)^{x} \cdot\left(\frac{25}{9}\right)^{x^{2}-12}=\left(\frac{27}{125}\right)^{3} $$

$$ 2^{x+1}+3 \cdot 2^{x-3}=76 $$

$$ 3 \cdot \sqrt[x]{81}-10 \cdot \sqrt[x]{9}+3=0 $$

$$ 3^{4 x+8}-4 \cdot 3^{2 x+5}+28=2 \log _{2} \sqrt{2} $$

$$ 2^{3 x-3}-5+6 \cdot 2^{3-3 x}=0 $$

$$ 3^{1-x}-3^{1+x}+9^{x}+9^{-x}=6 $$

$$ 64^{\frac{1}{x}}-2^{3+\frac{3}{x}}+12=0 $$

$$ 4^{\log _{9} x}-6 \cdot 2^{\log _{9} x}+2^{\log _{3} 27}=0 $$

$$ 4^{\sqrt{3 x^{2}-2 x}+1}+2=9 \cdot 2^{\sqrt{3 x^{2}-2 x}} $$

$$ 7 \cdot 4^{x^{2}}-9 \cdot 14^{x^{2}}+2 \cdot 49^{x^{2}}=0 $$

$$ 3 \cdot 16^{x}+36^{x}=2 \cdot 81^{x} $$

$$ 8^{x}+18^{x}=2 \cdot 27^{x} $$

$$ 6 \cdot \sqrt[x]{9}-13 \cdot \sqrt[x]{6}+6 \cdot \sqrt[x]{4}=0 $$

$$ 16^{x}-5 \cdot 8^{x}+6 \cdot 4^{x}=0 $$

$$ 27^{x}+12^{x}=2 \cdot 8^{x} $$

$$ (4+\sqrt{15})^{x}+(4-\sqrt{15})^{x}=62 $$

$$ (\sqrt{5+2 \sqrt{6}})^{x}+(\sqrt{5-2 \sqrt{6}})^{x}=10 $$

$$ \frac{1}{x+1}+\frac{2}{x+3}>\frac{3}{x+2} $$

$$ \left(\sqrt{a+\sqrt{a^{2}-1}}\right)^{x}+\left(\sqrt{a-\sqrt{a^{2}-1}}\right)^{x}=2 a $$

$$ 5^{1+x^{3}}-5^{1-x^{3}}=24 $$

$$ 5^{x-1}+5 \cdot\left(\frac{1}{5}\right)^{x-2}=26 $$

$$ 10^{\frac{2}{x}}+25^{\frac{1}{x}}=\frac{17}{4} \cdot 50^{\frac{1}{x}} $$

$$ 7^{\log _{7}\left(x^{2}-4 x+5\right)}=x-1 $$

$$ \log _{3}\left(x^{2}+4 x+12\right)=2 $$

$$ \log _{3} x+\log _{9} x+\log _{27} x=\frac{11}{2} $$

$$ \log _{2}(3-x)+\log _{2}(1-x)=3 $$

$$ \log (x-3)+\log (x+6)=1 $$

$$ \log (x-4)+\log (x+3)=\log (5 x+4) $$

$$ \ln \left(x^{3}+1\right)-\frac{1}{2} \ln \left(x^{2}+2 x+1\right)=\ln 3 $$

$$ \log _{5}(x-2)+2 \log _{5}\left(x^{3}-2\right)+\log _{5}(x-2)^{-1}=4 $$

$$ 2 \log _{3}(x-2)+\log _{3}(x-4)^{2}=0 $$

$$ \log _{2}(x+2)^{2}+\log _{2}(x+10)^{2}=4 \log _{2} 3 $$

$$ \log _{2}\left(\frac{x-2}{x-1}\right)-1=\log _{2}\left(\frac{3 x-7}{3 x-1}\right) $$

$$ 2 \log _{2}\left(\frac{x-7}{x-1}\right)+\log _{2}\left(\frac{x-1}{x+1}\right)=1 $$

$$ \log _{3}(5 x-2)-2 \log _{3} \sqrt{3 x+1}=1-\log _{3} 4 $$

$$ \log (3 x-2)-2=\frac{1}{2} \log (x+2)-\log 50 $$

$$ \log ^{2}\left(1+\frac{4}{x}\right)+\log ^{2}\left(1-\frac{4}{x+4}\right)=2 \log ^{2}\left(\frac{2}{x-1}-1\right) $$

$$ \log _{2} x^{4}+\log _{2} x^{2}=1 $$

$$ \log \left(10 x^{2}\right) \cdot \log x=1 $$

$$ \frac{\log _{2} x-1}{\log _{2} \frac{x}{2}}=2 \log _{2} \sqrt{x}+3-\log _{2}^{2} x $$

$$ 2 \log _{9} x+9 \log _{x} 3=10 $$

$$ \log _{x}(125 x) \cdot \log _{25}^{2} x=1 $$

$$ \log _{x} \sqrt{5}+\log _{x} 5 x=\frac{9}{4}+\log _{x}^{2} \sqrt{5} $$

$$ \log (\log x)+\log \left(\log x^{3}-2\right)=0 $$

$$ \sqrt{x-3}+\sqrt{1-x}>\sqrt{8 x-5} $$

$$ \log _{3 x+7}\left(9+12 x+4 x^{2}\right)=4-\log _{2 x+3}\left(6 x^{2}+23 x+21\right) $$