Question

logarithm: Find m^9^4

Answer 1

$3 log_{10}( \sqrt{m} ) + 2 log_{10}( \sqrt[3]{n}) - 1= 0 \\ log_{10}( {m}^{ \frac{3}{2} } ) + log_{10}( {n}^{ \frac{2}{3} } ) - log_{10}(10) = 0 \\ log_{10}( { m}^{ \frac{3}{2 } } \times {n}^{ \frac{2}{3} } ) - log_{10}(10) = 0 \\ {m}^{ \frac{3}{2}} \times {n}^{ \frac{2}{3} } = 10 \\ {m}^{9} \times {n}^{4} = {10}^{6}$