Question

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ho minh nha

\(\frac{7^{x+1}+7^{x+2}+7^x}{57}=\frac{5^{2x}+5^{2x+1}+5^{2x+3}}{131}\)

Answer 1

[ST]

\(\Leftrightarrow\frac{7^x.7+7^x.7^2+7^x}{57}=\frac{5^{2x}.1+5^{2x}.5+5^{2x}.5^3}{131}\)

\(\Leftrightarrow\frac{7^x\left(7+49+1\right)}{57}=\frac{5^{2x}\left(1+5+125\right)}{131}\)

\(\Leftrightarrow\frac{7^x.57}{57}=\frac{5^{2x}.131}{131}\)

<=> 7^x = 5^2x 

<=> \(\frac{7^x}{5^{2x}}=1\)

<=> \(\frac{7^x}{25^x}=1\)

<=> \(\left(\frac{7}{25}\right)^x=1\)

<=> x = 0