Question

Can we write ${125}^x+{45}^x={2.27}^x$ as ${\left(\frac{5}{3}\right)}^{3x}+{\left(\frac{5}{3}\right)}^x=2$

Answer 1

$\begin{array}{c}{125}^x+{45}^x={2.27}^x\\ 5^{3x}+(5\times 3^2{)}^x=2.(3^3{)}^x\\ 5^{3x}+5^x\times {3^2}^x=2.(3^3{)}^x\\ \frac{5^{3x}}{3^{3x}}+\frac{5^x}{3^x}=2\\ {\left(\frac{5}{3}\right)}^{3x}+{\left(\frac{5}{3}\right)}^x=2\end{array}$

Hence proved that we can write ${125}^x+{45}^x={2.27}^x$ as ${\left(\frac{5}{3}\right)}^{3x}+{\left(\frac{5}{3}\right)}^x=2$.