$$\begin{array}{rl}& 3^{2x-1}=3^{x+5}\\ \\ & {\cancel{3}}^{2x-1}={\cancel{3}}^{x+5}\\ \\ & 2x-1=x+5\\ \\ & x=6\end{array}$$

$$\begin{array}{rl}& 5^{x-4}=7^{x-4}\\ \\ & x-4=0\\ \\ & x=4\end{array}$$

$$\begin{array}{rl}& 5^{x-3}=2^{x+1}\\ \\ & \log 5^{x-3}=\log 2^{x+1}\\ \\ & (x-3).\log 5=(x+1).\log 2\\ \\ & x.\log 5-3\log 5=x.\log 2+\log 2\\ \\ & x.\log 5-x.\log 2=3\log 5+\log 2\\ \\ & x.(\log 5-\log 2)=3\log 5+\log 2\\ \\ & x=\frac{3\log 5+\log 2}{\log 5-\log 2}\end{array}$$

Faktor 1

$$\begin{array}{rl}& m-4=0\\ \\ & m=4\\ \\ & 2^x=2^2\\ \\ & x=2\end{array}$$

Faktor 2

$$\begin{array}{rl}& m-8=0\\ \\ & m=8\\ \\ & 2^x=2^3\\ \\ & x=3\end{array}$$

$(2x+3{)}^{x-1}=(3x+5{)}^{x-1}$

Solusi 1

$$\begin{array}{rl}& (2x+3{)}^{x-1}=(3x+5{)}^{x-1}\\ \\ & (2x+3{)}^{\cancel{x-1}}=(3x+5{)}^{\cancel{x-1}}\\ \\ & 2x+3=3x+5\\ \\ & x=-2\end{array}$$

Solusi 2

$$\begin{array}{rl}& x-1=0\\ \\ & x=1\end{array}$$

Uji $x=1$ apakah memenuhi $2x+3\ne 0$ dan $3x+5\ne 0$

$$\begin{array}{rl}& 2.1+3\ne 0\\ \\ & 3.1+5\ne 0\end{array}$$

$(x-5{)}^{x^2-4}=(x-5{)}^{2-x}$

Solusi 1

$$\begin{array}{rl}& (x-5{)}^{x^2-4}=(x-5{)}^{2-x}\\ \\ & {\cancel{(x-5)}}^{x^2-4}={\cancel{(x-5)}}^{2-x}\\ \\ & x^2-4=2-x\\ \\ & x^2+x-6=0\\ \\ & (x+3)(x-2)=0\\ \\ & x=-3\text{ atau }x=2\end{array}$$

Solusi 2

$$\begin{array}{rl}& (x-5{)}^{x^2-4}=(x-5{)}^{2-x}\\ \\ & x-5=1\\ \\ & x=6\end{array}$$

Solusi 3

$$\begin{array}{rl}& (x-5{)}^{x^2-4}=(x-5{)}^{2-x}\\ \\ & x-5=0\\ \\ & x=5\end{array}$$

Uji $x=5$ apakah memenuhi $x^2-4>0$ dan $2-x>0$.

$$\begin{array}{rl}& x^2-4=(5{)}^2-4=21>0\\ \\ & 2-x=2-5=-3<0\end{array}$$

Karena $2-x<0$, maka $x=5$ tidak memenuhi syarat.

Solusi 4

$$\begin{array}{rl}& (x-5{)}^{x^2-4}=(x-5{)}^{2-x}\\ \\ & x-5=-1\\ \\ & x=4\end{array}$$

Uji $x=5$ apakah memenuhi $x^2-4$ dan $2-x$ keduanya bilangan ganjil atau bilangan genap.

$$\begin{array}{rl}& x^2-4=(4{)}^2-4=12\text{genap}\\ \\ & 2-x=2-4=-2\text{genap}\end{array}$$

Karena $x^2-4$ dan $2-x$ bernilai genap, maka $x=4$ memenuhi syarat.

HP = $\{-3,2,4,6\}$