What is expand log_{10}(((a^3)/b)^5) ?

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

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expand log_{10}(((a^3)/b)^5)

expand

lo g_{10} ((\frac{a ^{3}}{b})^{5})

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

Solution steps

lo g_{10} ((\frac{a ^{3}}{b})^{5})

Apply log rule:

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

lo g_{10} ((\frac{a ^{3}}{b})^{5}) = 5 lo g_{10} (\frac{a ^{3}}{b})

= 5 lo g_{10} (\frac{a ^{3}}{b})

Apply log rule:

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

lo g_{10} (\frac{a ^{3}}{b}) = lo g_{10} (a^{3}) - lo g_{10} (b)

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

Apply log rule:

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

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

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

2 lo g_{N} (711.9) - lo g_{N} (7888.995)

ln (3 x^{6})

\frac{1}{2} ln ∣ 2 (8.5) + 1 ∣ + 2 ln ∣ 8.5 - 1 ∣ + c

ln (\frac{x ^{2} + y ^{2} - x}{x ^{2} + y ^{2} + x})

ln (\frac{1}{80})

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