Question

(64/125)^2 * (4/5)^4 * (16/25)^2x+1=(256/625)^3x Find value of x

Answer 1

$$\begin{gathered} {\left(\frac{64}{125}\right)}^2\times {\left(\frac{4}{5}\right)}^4\times {\left(\frac{16}{25}\right)}^{2x+1}={\left(\frac{256}{625}\right)}^{3x} \\ \Rightarrow {\left[{\left(\frac{4}{5}\right)}^3\right]}^2{\left(\frac{4}{5}\right)}^4\times {\left[{\left(\frac{4}{5}\right)}^2\right]}^{2x+1}={\left[{\left(\frac{4}{5}\right)}^4\right]}^{3x} \\ \Rightarrow {\left(\frac{4}{5}\right)}^6\times {\left(\frac{4}{5}\right)}^4\times {\left(\frac{4}{5}\right)}^{4x+2}={\left(\frac{4}{5}\right)}^{12x} \\ \Rightarrow {\left(\frac{4}{5}\right)}^{6+4+4x+2}={\left(\frac{4}{5}\right)}^{12x} \\ \Rightarrow {\left(\frac{4}{5}\right)}^{4x+12}={\left(\frac{4}{5}\right)}^{12x} \\ \Rightarrow 4x+12=12x \\ \Rightarrow 8x=12 \\ \Rightarrow x=\frac{12}{8}=\frac{3}{2} \end{gathered}$$