Question

5^x-4=6^x-4 решите уравнение

Answer 1

$5^{x-4} = 6^{x-4}$
$frac{ 5^{x} }{ 5^{4} } = frac{ 6^{x} }{ 6^{4} }$
$5^{x} * 6^{4} = 6^{x}* 5^{4}$
$5^{x} *1296= 6^{x} *625$
$5^{x} = frac{ 6^{x} *625}{1296}$
$5^{x}= 6^{x} * frac{ 5^{4} }{ 6^{4} }$
$frac{ 5^{x} }{ 6^{x} } = frac{ 5^{4} }{ 6^{4} }$
$( frac{5}{6}) ^{x} =( frac{5}{6}) ^{4}$
$x=4$
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