What is expand log_{10}((y^4)/(100x)) ?

The solution to expand log_{10}((y^4)/(100x)) is 4log_{10}(y)-2-log_{10}(x)

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expand log_{10}((y^4)/(100x))

expand

lo g_{10} (\frac{y ^{4}}{100 x})

4 lo g_{10} (y) - 2 - lo g_{10} (x)

Solution steps

lo g_{10} (\frac{y ^{4}}{100 x})

Apply log rule:

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

lo g_{10} (\frac{y ^{4}}{100 x}) = lo g_{10} (y^{4}) - lo g_{10} (100 x)

= lo g_{10} (y^{4}) - lo g_{10} (100 x)

Apply log rule:

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

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

= 4 lo g_{10} (y) - lo g_{10} (100 x)

Apply log rule:

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

lo g_{10} (100 x) = lo g_{10} (100) + lo g_{10} (x)

= 4 lo g_{10} (y) - (lo g_{10} (x) + lo g_{10} (100))

lo g_{10} (100) = 2

= 4 lo g_{10} (y) - (lo g_{10} (x) + 2)

- (2 + lo g_{10} (x)) : - 2 - lo g_{10} (x)

= 4 lo g_{10} (y) - 2 - lo g_{10} (x)

ln (8 e^{x})

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

lo g_{10} (\frac{1000}{x ^{2} + y ^{2}})

lo g_{10} (3 x^{5})

What is expand log_{10}((y^4)/(100x)) ?
The solution to expand log_{10}((y^4)/(100x)) is 4log_{10}(y)-2-log_{10}(x)