What is expand log_{4}((x^2)/5) ?

The solution to expand log_{4}((x^2)/5) is 2log_{4}(x)-log_{4}(5)

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expand log_{4}((x^2)/5)

expand

lo g_{4} (\frac{x ^{2}}{5})

2 lo g_{4} (x) - lo g_{4} (5)

Solution steps

lo g_{4} (\frac{x ^{2}}{5})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{4} (\frac{x ^{2}}{5}) = lo g_{4} (x^{2}) - lo g_{4} (5)

= lo g_{4} (x^{2}) - lo g_{4} (5)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{4} (x^{2}) = 2 lo g_{4} (x)

= 2 lo g_{4} (x) - lo g_{4} (5)

ln (x^{7}) - ln (x)

lo g_{10} (6) + lo g_{10} (5)

lo g_{7} (x y^{3})

- lo g_{10} (2.4 \cdot 1 0^{- 5})

lo g_{e} (\frac{1}{4})

What is expand log_{4}((x^2)/5) ?
The solution to expand log_{4}((x^2)/5) is 2log_{4}(x)-log_{4}(5)