What is expand log_{10}((x^9)/(y^4)) ?

The solution to expand log_{10}((x^9)/(y^4)) is 9log_{10}(x)-4log_{10}(y)

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expand log_{10}((x^9)/(y^4))

expand

lo g_{10} (\frac{x ^{9}}{y ^{4}})

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

Solution steps

lo g_{10} (\frac{x ^{9}}{y ^{4}})

Apply log rule:

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

lo g_{10} (\frac{x ^{9}}{y ^{4}}) = lo g_{10} (x^{9}) - lo g_{10} (y^{4})

= lo g_{10} (x^{9}) - lo g_{10} (y^{4})

Apply log rule:

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

lo g_{10} (x^{9}) = 9 lo g_{10} (x)

= 9 lo g_{10} (x) - lo g_{10} (y^{4})

Apply log rule:

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

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

= 9 lo g_{10} (x) - 4 lo g_{10} (y)

lo g_{10} (\frac{x}{y})

ln (\frac{25}{9})

lo g_{3} (\frac{9}{x + 5})

3 lo g_{a} (m) + 2 lo g_{a} (j) - 4 lo g_{a} (r)

2 (lo g_{6} (x) + lo g_{6} (y^{2})) - lo g_{6} (x + 2)

What is expand log_{10}((x^9)/(y^4)) ?
The solution to expand log_{10}((x^9)/(y^4)) is 9log_{10}(x)-4log_{10}(y)