What is expand log_{10}(((p^4)/(q^7))^2) ?

The solution to expand log_{10}(((p^4)/(q^7))^2) is 2(4log_{10}(p)-7log_{10}(q))

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expand log_{10}(((p^4)/(q^7))^2)

expand

lo g_{10} ((\frac{p ^{4}}{q ^{7}})^{2})

2 (4 lo g_{10} (p) - 7 lo g_{10} (q))

Solution steps

lo g_{10} ((\frac{p ^{4}}{q ^{7}})^{2})

Apply log rule:

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

lo g_{10} ((\frac{p ^{4}}{q ^{7}})^{2}) = 2 lo g_{10} (\frac{p ^{4}}{q ^{7}})

= 2 lo g_{10} (\frac{p ^{4}}{q ^{7}})

Apply log rule:

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

lo g_{10} (\frac{p ^{4}}{q ^{7}}) = lo g_{10} (p^{4}) - lo g_{10} (q^{7})

= 2 (lo g_{10} (p^{4}) - lo g_{10} (q^{7}))

Apply log rule:

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

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

= 2 (4 lo g_{10} (p) - lo g_{10} (q^{7}))

Apply log rule:

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

lo g_{10} (q^{7}) = 7 lo g_{10} (q)

= 2 (4 lo g_{10} (p) - 7 lo g_{10} (q))

- lo g_{10} (2.6 \cdot 1 0^{- 4})

lo g_{x} (\frac{1}{16})

3 ln (x) - 4 ln (y) - 5 ln (z)

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

5 lo g_{b} (x) + 3 lo g_{b} (z)

What is expand log_{10}(((p^4)/(q^7))^2) ?
The solution to expand log_{10}(((p^4)/(q^7))^2) is 2(4log_{10}(p)-7log_{10}(q))