What is 4log_{5}(x)-3log_{5}(y) ?

The solution to 4log_{5}(x)-3log_{5}(y) is log_{5}((x^4)/(y^3))

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simplify 4log_{5}(x)-3log_{5}(y)

simplify

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

lo g_{5} (\frac{x ^{4}}{y ^{3}})

Solution steps

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

Apply log rule:

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

4 lo g_{5} (x) = lo g_{5} (x^{4})

= lo g_{5} (x^{4}) - 3 lo g_{5} (y)

Apply log rule:

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

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

= lo g_{5} (x^{4}) - lo g_{5} (y^{3})

Apply log rule:

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

lo g_{5} (x^{4}) - lo g_{5} (y^{3}) = lo g_{5} (\frac{x ^{4}}{y ^{3}})

= lo g_{5} (\frac{x ^{4}}{y ^{3}})

0.026 ln (0.095) + 0.416 ln (10)

- ln (\frac{1}{2})

lo g_{2} (3) + 4 lo g_{2} (x) - 2 lo g_{2} (y)

lo g_{10} (a) + 2 lo g_{10} (b) - 3 lo g_{10} (c)

ln ((\frac{1}{x})^{\frac{1}{l n ( x )}})

What is 4log_{5}(x)-3log_{5}(y) ?
The solution to 4log_{5}(x)-3log_{5}(y) is log_{5}((x^4)/(y^3))