What is log_{10}(x/(q(z-9)^2)) ?

The solution to log_{10}(x/(q(z-9)^2)) is log_{10}(x)-log_{10}(q)-2log_{10}(z-9)

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simplify log_{10}(x/(q(z-9)^2))

simplify

lo g_{10} (\frac{x}{q ( z - 9 ) ^{2}})

lo g_{10} (x) - lo g_{10} (q) - 2 lo g_{10} (z - 9)

Solution steps

lo g_{10} (\frac{x}{q ( z - 9 ) ^{2}})

Apply log rule:

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

lo g_{10} (\frac{x}{q ( z - 9 ) ^{2}}) = lo g_{10} (x) - lo g_{10} (q (z - 9)^{2})

= lo g_{10} (x) - lo g_{10} (q (z - 9)^{2})

Apply log rule:

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

lo g_{10} (q (z - 9)^{2}) = lo g_{10} (q) + lo g_{10} ((z - 9)^{2})

= lo g_{10} (x) - (lo g_{10} (q) + lo g_{10} ((z - 9)^{2}))

Apply log rule:

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

lo g_{10} ((z - 9)^{2}) = 2 lo g_{10} (z - 9)

= lo g_{10} (x) - (lo g_{10} (q) + 2 lo g_{10} (z - 9))

- (lo g_{10} (q) + 2 lo g_{10} (z - 9)) : - lo g_{10} (q) - 2 lo g_{10} (z - 9)

= lo g_{10} (x) - lo g_{10} (q) - 2 lo g_{10} (z - 9)

lo g_{3} (\frac{27}{x + 8})

ln (x^{2} y^{5} z)

ln (20) - ln (5)

4 lo g_{10} (2) + 4 lo g_{10} (x)

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

What is log_{10}(x/(q(z-9)^2)) ?
The solution to log_{10}(x/(q(z-9)^2)) is log_{10}(x)-log_{10}(q)-2log_{10}(z-9)