Question

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Answer 1

$\tt We\:know\:that \:by\: defination \:of \:log \\ \\ \tt \boxed{\bold{\underline{\green{\tt If\: {log}_{x}{y} = a \: \implies {x}^{a} = y }}}} \\ \\ \tt (a)\:if\: {log}_{3}{x} = 4 \\ \\ \tt \implies {3}^{4} = x \\ \\ \tt \implies x = 81 \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt x = 81 }}}} \\ \\ \tt (b) \:if \:{log}_{5}{125}=x \\ \\ \tt \implies {5}^{x} = 125 \\ \\ \tt \implies {5}^{x} = {5}^{3} \\ \\ \tt \therefore \boxed{\bold{\underline{\red{\tt x = 3}}}} \\ \\ \orange{\mathbb{PROPERTIES\ OF\: LOGARITHM }} \\ \\ \tt \circ \:\: {log}_{x}{a} + {log}_{x}{b} = {log}_{x}{(ab)} \\ \\ \tt \circ \:\: {log}_{x}{a} - {log}_{x}{b} = {log}_{x}{(\frac{a}{b})} \\ \\ \tt \circ \:\: {log}_{x}{{x}^{a}} = a \\ \\ \tt \circ \:\: {x}^{{log}_{x}{a}} = a$