Question

Find the value of x
${13}^{ \sqrt{x } } = {4}^{4} - {3}^{4} - 6$
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Answer 1

${13}^{ \sqrt{x } } = {4}^{4} - {3}^{4} - 6 \\ \\ {13}^{ \sqrt{x} } = ({4}^{2{}^{2} } ) - ({3}^{2 {}^{2} } ) - 6 \\ \\ {13}^{ \sqrt{x} } = {16}^{2} - {9}^{2} - 6 \\ \\ {13}^{ \sqrt{x} } = 256 - 81 - 6 \\ \\ {13}^{ \sqrt{x} } = 256 - 87 \\ \\ {13}^{ \sqrt{x} } = 169 \\ \\ 169 = 13 \times 13 \\ \\ {13}^{ \sqrt{x} } = {13}^{2}$

As we Know

${x}^{a} = {x}^{b} \\ \\ a = b$

${13}^{ \sqrt{x} } = {13}^{2} \\ \\ \sqrt{x } = 2$

Squaring Both Sides

$\sqrt{x} {}^{2} = {2}^{2} \\ \\ x = 4$

$\underline{\mathbf{\huge{X=4}}}$