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If value of 8power x+1 = 64 what is the value of 3 power 2x +1 |
| Answer» ION is 27.Step-by-step explanation:It has been GIVEN that8^{x+1}=648 x+1 =64Take log both sides\log(8^{x+1})=\log64log(8 x+1 )=log64Apply the log rule \log x^y=y\log xlogx y =ylogx(x+1)\log8)=\log64(x+1)log8)=log64Divide both sides by log 8\begin{gathered}x+1=\frac{\log64}{\log8}\\\\x+1=\frac{\log8^2}{\log8}\\\\x+1=\frac{2\log8}{\log8}\\\\x+1=2\\\\x=1\end{gathered} x+1= log8log64 x+1= log8log8 2 x+1= log82log8 x+1=2x=1Now, we have to find the VALUE of the EXPRESSION3^{2x+1}3 2x+1Substitute x = 1\begin{gathered}3^{2\cdot1+1}\\\\=3^{2+1}\\\\=3^3\\\\=27\end{gathered} 3 2⋅1+1 =3 2+1 =3 3 =27 | |