What is expand log_{10}((3x^4)/t) ?

The solution to expand log_{10}((3x^4)/t) is log_{10}(3)+4log_{10}(x)-log_{10}(t)

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expand log_{10}((3x^4)/t)

expand

lo g_{10} (\frac{3 x ^{4}}{t})

lo g_{10} (3) + 4 lo g_{10} (x) - lo g_{10} (t)

Solution steps

lo g_{10} (\frac{3 x ^{4}}{t})

Apply log rule:

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

lo g_{10} (\frac{3 x ^{4}}{t}) = lo g_{10} (3 x^{4}) - lo g_{10} (t)

= lo g_{10} (3 x^{4}) - lo g_{10} (t)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (3 x^{4}) = lo g_{10} (3) + lo g_{10} (x^{4})

= lo g_{10} (3) + lo g_{10} (x^{4}) - lo g_{10} (t)

Apply log rule:

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

lo g_{10} (x^{4}) = 4 lo g_{10} (x)

= lo g_{10} (3) + 4 lo g_{10} (x) - lo g_{10} (t)

lo g_{2} (\frac{- 3 m ^{2} n ^{4}}{4 p})

lo g_{3} (\frac{27}{x + 2})

ln (5) + 5 ln (3)

\frac{1}{2} (lo g_{5} (x^{6}) + lo g_{5} (x^{3}))

What is expand log_{10}((3x^4)/t) ?
The solution to expand log_{10}((3x^4)/t) is log_{10}(3)+4log_{10}(x)-log_{10}(t)