What is log_{10}((a^2b^{1/3})/(c^4)) ?

The solution to log_{10}((a^2b^{1/3})/(c^4)) is 2log_{10}(a)+1/3 log_{10}(b)-4log_{10}(c)

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simplify log_{10}((a^2b^{1/3})/(c^4))

simplify

lo g_{10} (\frac{a ^{2} b ^{\frac{1}{3}}}{c ^{4}})

2 lo g_{10} (a) + \frac{1}{3} lo g_{10} (b) - 4 lo g_{10} (c)

Solution steps

lo g_{10} (\frac{a ^{2} b ^{\frac{1}{3}}}{c ^{4}})

Apply log rule:

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

lo g_{10} (\frac{a ^{2} b ^{\frac{1}{3}}}{c ^{4}}) = lo g_{10} (a^{2} b^{\frac{1}{3}}) - lo g_{10} (c^{4})

= lo g_{10} (a^{2} b^{\frac{1}{3}}) - lo g_{10} (c^{4})

lo g_{10} (a^{2} b^{\frac{1}{3}}) = 2 lo g_{10} (a) + \frac{1}{3} lo g_{10} (b)

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

= 2 lo g_{10} (a) + \frac{1}{3} lo g_{10} (b) - 4 lo g_{10} (c)

10 ln (x^{2} y^{5} z^{3}) - λ (5 x + 2 y + 8 z)

lo g_{10} (y x^{5})

7 lo g_{3} (u) + 4 lo g_{3} (v)

- 1.46 - 5 lo g_{10} (\frac{152.67}{10})

3 ln (x) - 5 ln (\frac{1}{y}) - 4 ln (x y)

What is log_{10}((a^2b^{1/3})/(c^4)) ?
The solution to log_{10}((a^2b^{1/3})/(c^4)) is 2log_{10}(a)+1/3 log_{10}(b)-4log_{10}(c)