Question

Write 1/3log 27 + (1 )/4log 625 – 2log 8 as the logarithm of a single number.

Answer 1

$heya \\ \\ \\ we \: know \: that \\ \\ log(x {}^{n} ) = n log(x) \\ \\ \\ \\ \\ \\ \\ \\ (1\div 3) log(3 {}^{3} ) + (1 \div 4) log(5 {}^{4} ) - 2 log(2 {}^{3} ) \\ \\ \\ (3 \div 3) log(3) + (4 \div 4) log(4) - 6 log(2) \\ \\ \\ log(3) + log(4) - 6 log(2) \\ \\ \\ log(3) + 2 log(2) - 6 log(2) \\ \\ \\ log(3) - 4 log(2) \\ \\ \\ \\ log(3 \div 16)$