What is 19log_{3}(x)-82log_{3}(y)+log_{3}(z) ?

The solution to 19log_{3}(x)-82log_{3}(y)+log_{3}(z) is log_{3}((x^{19}z)/(y^{82)})

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simplify 19log_{3}(x)-82log_{3}(y)+log_{3}(z)

simplify

19 lo g_{3} (x) - 82 lo g_{3} (y) + lo g_{3} (z)

lo g_{3} (\frac{x ^{19} z}{y ^{82}})

Solution steps

19 lo g_{3} (x) - 82 lo g_{3} (y) + lo g_{3} (z)

Apply log rule:

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

19 lo g_{3} (x) = lo g_{3} (x^{19})

= lo g_{3} (x^{19}) - 82 lo g_{3} (y) + lo g_{3} (z)

Apply log rule:

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

82 lo g_{3} (y) = lo g_{3} (y^{82})

= lo g_{3} (x^{19}) - lo g_{3} (y^{82}) + lo g_{3} (z)

Apply log rule:

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

lo g_{3} (x^{19}) - lo g_{3} (y^{82}) = lo g_{3} (\frac{x ^{19}}{y ^{82}})

= lo g_{3} (\frac{x ^{19}}{y ^{82}}) + lo g_{3} (z)

Apply log rule:

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

lo g_{3} (\frac{x ^{19}}{y ^{82}}) + lo g_{3} (z) = lo g_{3} (\frac{x ^{19}}{y ^{82}} z)

= lo g_{3} (\frac{x ^{19}}{y ^{82}} z)

Multiply fractions:

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

= lo g_{3} (\frac{x ^{19} z}{y ^{82}})

lo g_{2} ((\frac{6 ^{4}}{11})^{5})

lo g_{10} (2 ab)

ln (ye)

ln (2) + 2 ln (x) - ln (9) - 5 ln (y) - 6 ln (z - 4)

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

What is 19log_{3}(x)-82log_{3}(y)+log_{3}(z) ?
The solution to 19log_{3}(x)-82log_{3}(y)+log_{3}(z) is log_{3}((x^{19}z)/(y^{82)})