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Answer 1

${2}^{x - 7} \times {5}^{x - 4} = 1250 \\ {2}^{x} . {2}^{ - 7} \times {5}^{x} .{5}^{ - 4} = {5}^{4} \times 2 \\ {(2.5)}^{x} \times {2 }^{ - 7} \times {5}^{ - 4} = {5}^{4} \times 2 \\ {(10)}^{x} = {2}^{7} \times {5}^{4} \times {5}^{4} \times 2 \\ {10}^{x} = {2}^{7 + 1} \times {5}^{4 + 4} \\ {10}^{x} = {2}^{8} \times {5}^{8} \\ {10}^{x} = {(2.5)}^{8} \\ {10}^{x} = {10}^{8} \\ x = 8$


${13}^{ \sqrt{x} } = {4}^{4} - { 3}^{4} - 6 \\ {13}^{ \sqrt{x} } = 256 - 81 - 6 \\ {13}^{ \sqrt{x} } = 256 - 87 \\ {13}^{ \sqrt{x} } = 169 \\ {13}^{ \sqrt{x} } = {13}^{2} \\ \sqrt{x} = 2 \\ x = 4$


${ (\sqrt{ \frac{3}{5} }) }^{(x + 1)} = \frac{125}{27} \\ {( \sqrt{ \frac{3}{5} } )}^{(x + 1)} = {( \frac{ 5}{3} )}^{3} \\ {( \sqrt{ \frac{3}{5} } )}^{(x + 1)} = {( \sqrt{ \frac{5}{3} } ) }^{ - 6} \\ x + 1 = - 6 \\ x = - 6 - 1 \\ x = - 7$