a. Nilai [tex] x [/tex] dari [tex] 25^{x-2} = 5^{x+3} [/tex]
[tex] \begin{align} 25^{x-2} &= 5^{x+3} \\ 5^{2(x-2)} &= 5^{x+3} \\ \Rightarrow 2(x-2) &= x+3 \\ 2x-4 &= x+3 \\ 2x-x &= 3+4 \\ x &= 7 \end{align} [/tex]
b. Nilai [tex] x [/tex] dari [tex] (\frac{1}{9})^{2x-1} = 27^{2-x} [/tex]
[tex] \begin{align} \left(\frac{1}{9}\right)^{2x-1} &= 27^{2-x} \\ 3^{-2(2x-1)} &= 3^{3(2-x)} \\ \Rightarrow -2(2x-1) &= 3(2-x) \\ -4x+2 &= 6-3x \\ -4x+3x &= 6-2 \\ -x &= 4 \\ x &= -4 \end{align} [/tex]
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a. Nilai [tex] x [/tex] dari [tex] 25^{x-2} = 5^{x+3} [/tex]
[tex] \begin{align} 25^{x-2} &= 5^{x+3} \\ 5^{2(x-2)} &= 5^{x+3} \\ \Rightarrow 2(x-2) &= x+3 \\ 2x-4 &= x+3 \\ 2x-x &= 3+4 \\ x &= 7 \end{align} [/tex]
b. Nilai [tex] x [/tex] dari [tex] (\frac{1}{9})^{2x-1} = 27^{2-x} [/tex]
[tex] \begin{align} \left(\frac{1}{9}\right)^{2x-1} &= 27^{2-x} \\ 3^{-2(2x-1)} &= 3^{3(2-x)} \\ \Rightarrow -2(2x-1) &= 3(2-x) \\ -4x+2 &= 6-3x \\ -4x+3x &= 6-2 \\ -x &= 4 \\ x &= -4 \end{align} [/tex]