Find x.
5^2x - 7^x - 5^2x (35) + 7^x (35) = 0

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Please find below the solution to the asked query:

$$\begin{gathered} 5^{2\mathrm{x}}-7^{\mathrm{x}}-5^{2\mathrm{x}}\left(35\right)+7^{\mathrm{x}}\left(35\right)=0 \\ \Rightarrow 7^{\mathrm{x}}\left(35\right)-7^{\mathrm{x}}+5^{2\mathrm{x}}-5^{2\mathrm{x}}\left(35\right)=0 \\ \Rightarrow 7^{\mathrm{x}}\left(35-1\right)-5^{2\mathrm{x}}\left(35-1\right)=0 \\ \Rightarrow \left(35-1\right)\left(7^{\mathrm{x}}-5^{2\mathrm{x}}\right)=0 \\ \Rightarrow 7^{\mathrm{x}}-5^{2\mathrm{x}}=0 \\ \Rightarrow 7^{\mathrm{x}}=5^{2\mathrm{x}} \\ \mathrm{As} \mathrm{powers} \mathrm{of} 7 \mathrm{end} \mathrm{with} 7,9,3,1 \mathrm{while} \mathrm{powers} \mathrm{of} 5 \mathrm{always} \mathrm{end} \mathrm{with} 5, \mathrm{hence} \\ {7}^{\mathrm{x}}=5^{2\mathrm{x}} \mathrm{is} \mathrm{possible} \mathrm{only} \mathrm{when} \\ 2\mathrm{x}=\mathrm{x}=0 \\ \mathbf{Hence}\mathbf{ }\mathbf{x}\mathbf{=}\mathbf{0}\mathbf{ }\left(\mathbf{Answer}\right) \end{gathered}$$

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