Tentukan himpunan dari persamaan eksponen berikut :
1.![\sqrt[4]{ 9^{x+1} } = 27^ \frac{1}{2}](https://tex.z-dn.net/?f=+%5Csqrt%5B4%5D%7B+9%5E%7Bx%2B1%7D+%7D+%3D+27%5E+%5Cfrac%7B1%7D%7B2%7D+ "\sqrt[4]{ 9^{x+1} } = 27^ \frac{1}{2}")
2.![3^{2x+1} = \sqrt[4]{27 x^{3x-2} }](https://tex.z-dn.net/?f=+3%5E%7B2x%2B1%7D+%3D+%5Csqrt%5B4%5D%7B27+x%5E%7B3x-2%7D+%7D+ "3^{2x+1} = \sqrt[4]{27 x^{3x-2} }")
3.![\sqrt[3]{5 x^{2x-1} } = 5^{3x+2}](https://tex.z-dn.net/?f=+%5Csqrt%5B3%5D%7B5+x%5E%7B2x-1%7D+%7D+%3D+5%5E%7B3x%2B2%7D+ "\sqrt[3]{5 x^{2x-1} } = 5^{3x+2}")
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MicoArrafi
![$\begin{align} \sqrt[4]{9^{x+1}}&=27^{\frac{1}{2}}\\\sqrt[4]{3^{2(x+1)}}&=\sqrt{27}\\\sqrt{3^{x+1}}&=\sqrt{3^3}\\3^{x+1}&=3^3\\x+1&=3\\x&=3-1\\x&=\bold2 \end](https://tex.z-dn.net/?f=%24%5Cbegin%7Balign%7D+%5Csqrt%5B4%5D%7B9%5E%7Bx%2B1%7D%7D%26%3D27%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C%5Csqrt%5B4%5D%7B3%5E%7B2%28x%2B1%29%7D%7D%26%3D%5Csqrt%7B27%7D%5C%5C%5Csqrt%7B3%5E%7Bx%2B1%7D%7D%26%3D%5Csqrt%7B3%5E3%7D%5C%5C3%5E%7Bx%2B1%7D%26%3D3%5E3%5C%5Cx%2B1%26%3D3%5C%5Cx%26%3D3-1%5C%5Cx%26%3D%5Cbold2+%5Cend "$\begin{align} \sqrt[4]{9^{x+1}}&=27^{\frac{1}{2}}\\\sqrt[4]{3^{2(x+1)}}&=\sqrt{27}\\\sqrt{3^{x+1}}&=\sqrt{3^3}\\3^{x+1}&=3^3\\x+1&=3\\x&=3-1\\x&=\bold2 \end")
2 votes
Thanks 1
karrina
akar 4 nya hilang yaa ?
MicoArrafi
Iya, karena di dalamnya ada pangkat 2, sehingga akarnya menjadi akar pangkat 2
karrina
oh iya, makasih ya :)
MicoArrafi
Iya, sama-sama :)