What is 3log_{5}(x)-18log_{5}(y) ?

The solution to 3log_{5}(x)-18log_{5}(y) is log_{5}((x^3)/(y^{18)})

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simplify 3log_{5}(x)-18log_{5}(y)

simplify

3 lo g_{5} (x) - 18 lo g_{5} (y)

lo g_{5} (\frac{x ^{3}}{y ^{18}})

Solution steps

3 lo g_{5} (x) - 18 lo g_{5} (y)

Apply log rule:

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

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

= lo g_{5} (x^{3}) - 18 lo g_{5} (y)

Apply log rule:

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

18 lo g_{5} (y) = lo g_{5} (y^{18})

= lo g_{5} (x^{3}) - lo g_{5} (y^{18})

Apply log rule:

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

lo g_{5} (x^{3}) - lo g_{5} (y^{18}) = lo g_{5} (\frac{x ^{3}}{y ^{18}})

= lo g_{5} (\frac{x ^{3}}{y ^{18}})

lo g_{5} (\frac{25}{x + 8})

ln (x^{2} - 49) - ln (x + 7)

lo g_{10} (x \cdot y)

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

- 2 lo g_{\frac{1024}{5}} (50)

What is 3log_{5}(x)-18log_{5}(y) ?
The solution to 3log_{5}(x)-18log_{5}(y) is log_{5}((x^3)/(y^{18)})