What is log_{10}(x)-4log_{10}(y)+9log_{10}(z) ?

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

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simplify log_{10}(x)-4log_{10}(y)+9log_{10}(z)

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

ln (\frac{16}{6})

lo g_{3} (\frac{1}{25 \cdot 3 \cdot 5 ^{53}})

ln (ln (y)) + ln (x)

lo g_{y} (2 e^{5}) - lo g_{y} (5 e^{8})

\frac{3}{4} (ln (7) - ln (5))

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