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3.6: Експоненціальні рівняння
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$\begin{aligned} 16^{x} &=25 \\ \log 16^{x} &=\log 25 \\ x \log 16 &=\log 25 \\ x &=\frac{\log 25}{\log 16} \\ x &=1.16 \end{aligned}$ \(\begin{aligned} \log (x+1)^{(x-4)} &=\log 1 \\(x-4) \cdot \lo... $\begin{aligned} 16^{x} &=25 \\ \log 16^{x} &=\log 25 \\ x \log 16 &=\log 25 \\ x &=\frac{\log 25}{\log 16} \\ x &=1.16 \end{aligned}$ $\begin{aligned} \log (x+1)^{(x-4)} &=\log 1 \\(x-4) \cdot \log (x+1) &=0 \\ x-4=0 & \text { or } \log (x+1)=0 \\ x=& 4 \text { or }(x+1)=10^{0}=1 \\ & x=4,0 \end{aligned}$ $\begin{aligned} \frac{e^{x}-e^{-x}}{3} &=14 \\ e^{x}\left(e^{x}-e^{-x}\right) &=(42) e^{x} \\ e^{2 x}-1 &=42 e^{x} \\\left(e^{x}\right)^{2}-42 e^{x}-1 &=0 \end{aligned}$