Solve ${(x^{{log}_{10} 3})}^{2} - (3^{{log}_{10} x}) - 2 = 0$
Find the sum of all possible values of x

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Solution

${(x^{{log}_{10} 3})}^{2} - (3^{{log}_{10} x}) - 2 = 0$
$\Rightarrow {(x^{{log}_{10} 3})}^{2} - (x^{{log}_{10} 3}) - 2 = 0$
$\Rightarrow x^{{log}_{10} 3} = - 2, 1$
$\Rightarrow x = 1$

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Solve (xlog103)2−(3log10x)−2=0Find the sum of all possible values of x

(xlog103)2−(3log10x)−2=0⇒(xlog103)2−(xlog103)−2=0⇒xlog103=−2,1⇒x=1

Solve ${(x^{{log}_{10} 3})}^{2} - (3^{{log}_{10} x}) - 2 = 0$
Find the sum of all possible values of x

${(x^{{log}_{10} 3})}^{2} - (3^{{log}_{10} x}) - 2 = 0$
$\Rightarrow {(x^{{log}_{10} 3})}^{2} - (x^{{log}_{10} 3}) - 2 = 0$
$\Rightarrow x^{{log}_{10} 3} = - 2, 1$
$\Rightarrow x = 1$