What is log_{4}((3a^7c)/5) ?

The solution to log_{4}((3a^7c)/5) is log_{4}(3)+7log_{4}(a)+log_{4}(c)-log_{4}(5)

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simplify log_{4}((3a^7c)/5)

simplify

lo g_{4} (\frac{3 a ^{7} c}{5})

lo g_{4} (3) + 7 lo g_{4} (a) + lo g_{4} (c) - lo g_{4} (5)

Solution steps

lo g_{4} (\frac{3 a ^{7} c}{5})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{4} (\frac{3 a ^{7} c}{5}) = lo g_{4} (3 a^{7} c) - lo g_{4} (5)

= lo g_{4} (3 a^{7} c) - lo g_{4} (5)

Simplify

lo g_{4} (3 a^{7} c) : lo g_{4} (3) + 7 lo g_{4} (a) + lo g_{4} (c)

= lo g_{4} (3) + 7 lo g_{4} (a) + lo g_{4} (c) - lo g_{4} (5)

ln (x) - ln (7)

lo g_{2} (\frac{x ^{3} y ^{2}}{z})

3 ln (a) - \frac{1}{2} ln (b) + 5 ln (c) - 7 ln (d)

lo g_{2} (x^{2} - 25) + lo g_{2} (x - 6)

ln (\frac{x ^{9} x ^{2} + 1}{( x + 1 ) ^{9}})

What is log_{4}((3a^7c)/5) ?
The solution to log_{4}((3a^7c)/5) is log_{4}(3)+7log_{4}(a)+log_{4}(c)-log_{4}(5)