What is expand log_{10}(((ab)^3)/(c^5)) ?

The solution to expand log_{10}(((ab)^3)/(c^5)) is 3log_{10}(a)+3log_{10}(b)-5log_{10}(c)

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expand log_{10}(((ab)^3)/(c^5))

expand

lo g_{10} (\frac{( ab ) ^{3}}{c ^{5}})

3 lo g_{10} (a) + 3 lo g_{10} (b) - 5 lo g_{10} (c)

Solution steps

lo g_{10} (\frac{( ab ) ^{3}}{c ^{5}})

Apply log rule:

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

lo g_{10} (\frac{( ab ) ^{3}}{c ^{5}}) = lo g_{10} ((ab)^{3}) - lo g_{10} (c^{5})

= lo g_{10} ((ab)^{3}) - lo g_{10} (c^{5})

Apply log rule:

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

lo g_{10} ((ab)^{3}) = 3 lo g_{10} (ab)

= 3 lo g_{10} (ab) - lo g_{10} (c^{5})

Apply log rule:

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

lo g_{10} (c^{5}) = 5 lo g_{10} (c)

= 3 lo g_{10} (ab) - 5 lo g_{10} (c)

Apply log rule:

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

3 lo g_{10} (ab) = 3 lo g_{10} (a) + 3 lo g_{10} (b)

= 3 lo g_{10} (a) + 3 lo g_{10} (b) - 5 lo g_{10} (c)

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

+ 9 ln (y) + 4 ln (2 x - 1) + 5 ln (x - 1)

\frac{1}{2} ln (2) + \frac{1}{2} ln (3)

- \frac{1}{3} (ln (7) - ln (26))

10 lo g_{10} (\frac{2}{1}) + 10 lo g_{10} (\frac{0.007}{1}) + 52

What is expand log_{10}(((ab)^3)/(c^5)) ?
The solution to expand log_{10}(((ab)^3)/(c^5)) is 3log_{10}(a)+3log_{10}(b)-5log_{10}(c)