Question

PLZ TELL ME THE VALUE OF K also solve it step by step

Answer 1

$\huge \underline \mathfrak{answer}$

$( \frac{ -4 }{ 5 } ) ^ { 2 } \times ( \frac{ 4 }{ 5 } ) ^ { 5 } =( \frac{ 4 }{ 5 } ) ^ { 6k+1 }\\ \\\left(-\frac{4}{5}\right)^{2}\times \left(\frac{4}{5}\right)^{5}=\left(\frac{4}{5}\right)^{6k+1} \\ \\\frac{16}{25}\times \left(\frac{4}{5}\right)^{5}=\left(\frac{4}{5}\right)^{6k+1} \\ \\\frac{16}{25}\times \left(\frac{1024}{3125}\right)=\left(\frac{4}{5}\right)^{6k+1} \\ \\\frac{16384}{78125}=\left(\frac{4}{5}\right)^{6k+1} \\ \\\left(\frac{4}{5}\right)^{6k+1}=\frac{16384}{78125} \\ \\\log(\left(\frac{4}{5}\right)^{6k+1})=\log(\frac{16384}{78125}) \\ \\\left(6k+1\right)\log(\frac{4}{5})=\log(\frac{16384}{78125}) \\ \\6k+1=\frac{\log(\frac{16384}{78125})}{\log(\frac{4}{5})} \\ \\6k+1=\log_{\frac{4}{5}}\left(\frac{16384}{78125}\right) \\ \\6k=7-1 \\ \\k=\frac{6}{6}$

$\huge \ \mathfrak{@DarkShadow7083 }$

Answer 2

$\huge \underline \mathfrak{Answer}$

$</p><p>\begin{gathered} \implies( \frac{ -4 }{ 5 } ) ^ { 2 } \times ( \frac{ 4 }{ 5 } ) ^ { 5 } =( \frac{ 4 }{ 5 } ) ^ { 6k+1 }\\ \\\left(-\frac{4}{5}\right)^{2}\times \left(\frac{4}{5}\right)^{5}=\left(\frac{4}{5}\right)^{6k+1} \\ \\\frac{16}{25}\times \left(\frac{4}{5}\right)^{5}=\left(\frac{4}{5}\right)^{6k+1} \\ \\\frac{16}{25}\times \left(\frac{1024}{3125}\right)=\left(\frac{4}{5}\right)^{6k+1} \\ \\\frac{16384}{78125}=\left(\frac{4}{5}\right)^{6k+1} \\ \\\left(\frac{4}{5}\right)^{6k+1}=\frac{16384}{78125} \\ \\\log(\left(\frac{4}{5}\right)^{6k+1})=\log(\frac{16384}{78125}) \\ \\\left(6k+1\right)\log(\frac{4}{5})=\log(\frac{16384}{78125}) \\ \\ \sf \: \implies6k+1=\frac{\log(\frac{16384}{78125})}{\log(\frac{4}{5})} \\ \ \\ \sf \implies \: 6k+1=\log_{\frac{4}{5}}\left(\frac{16384}{78125}\right) \\ \\ \sf\implies \: 6k=7-1 \\ \\ \implies \sf k=\frac{6}{6}\end{gathered}$