What is expand log_{10}((R^5S^4)/(Z^6)) ?

The solution to expand log_{10}((R^5S^4)/(Z^6)) is 5log_{10}(R)+4log_{10}(S)-6log_{10}(Z)

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expand log_{10}((R^5S^4)/(Z^6))

expand

lo g_{10} (\frac{R ^{5} S ^{4}}{Z ^{6}})

5 lo g_{10} (R) + 4 lo g_{10} (S) - 6 lo g_{10} (Z)

Solution steps

lo g_{10} (\frac{R ^{5} S ^{4}}{Z ^{6}})

Apply log rule:

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

lo g_{10} (\frac{R ^{5} S ^{4}}{Z ^{6}}) = lo g_{10} (R^{5} S^{4}) - lo g_{10} (Z^{6})

= lo g_{10} (R^{5} S^{4}) - lo g_{10} (Z^{6})

Apply log rule:

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

lo g_{10} (Z^{6}) = 6 lo g_{10} (Z)

= lo g_{10} (R^{5} S^{4}) - 6 lo g_{10} (Z)

Apply log rule:

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

lo g_{10} (R^{5} S^{4}) = lo g_{10} (R^{5}) + lo g_{10} (S^{4})

= lo g_{10} (R^{5}) + lo g_{10} (S^{4}) - 6 lo g_{10} (Z)

Apply log rule:

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

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

= 5 lo g_{10} (R) + lo g_{10} (S^{4}) - 6 lo g_{10} (Z)

Apply log rule:

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

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

= 5 lo g_{10} (R) + 4 lo g_{10} (S) - 6 lo g_{10} (Z)

ln (\frac{1}{x + 1})

ln (x) - ln (x - 1)

lo g_{10} (\frac{2 ^{4}}{5})

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

lo g_{b} (y z^{4})

What is expand log_{10}((R^5S^4)/(Z^6)) ?
The solution to expand log_{10}((R^5S^4)/(Z^6)) is 5log_{10}(R)+4log_{10}(S)-6log_{10}(Z)