Question

find x if 1/2
log 10(11+4√7) = log10 (2+ x)


wrong answer would be reported​

Answer 1

Step-by-step explanation:

We have,

$\frac{1}{2} log_{10}(11 + 4 \sqrt{7} ) = log_{10}(2 + x)$

$\implies log_{10}( \sqrt{11 + 4 \sqrt{7} } ) = log_{10}(2 + x)$

$\implies \sqrt{11 + 4 \sqrt{7} } = 2 + x$

$\implies \sqrt{7 + 4 + 2 \times 2 \times \sqrt{7} } = 2 + x$

$\implies \sqrt{ (\sqrt{7})^{2} + ( {2})^{2} + 2 \times 2 \times \sqrt{7} } = 2 + x$

$\implies \sqrt{(2 + \sqrt{7}) ^{2} } = 2 + x$

$\implies2 + \sqrt{7} = 2 + x$

$\implies \: x = \sqrt{7}$