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Chain Rule of Differentiation

x log10 10/3...

Question

$x l o g_{10} (10 / 3) + l o g_{10} 3 = l o g_{10} (2 + 3^{x}) + x$

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Solution

$3^{1 - x} = 2 + 3^{x}$
or $\frac{3}{t} = 2 + t o r t^{2} + 2 t - 3 = 0$
or $(t + 3) (t - 1) = 0$
$∴ t = 3^{x} = - 3 o r 1$
$∴ 3^{x} = 1 = 3^{0} o r x = 0.$ $(3^{x} = - 3 r e j e c t e d)$

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