What is 12log_{7}(x)-3log_{7}(y) ?

The solution to 12log_{7}(x)-3log_{7}(y) is log_{7}((x^{12})/(y^3))

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simplify 12log_{7}(x)-3log_{7}(y)

simplify

12 lo g_{7} (x) - 3 lo g_{7} (y)

lo g_{7} (\frac{x ^{12}}{y ^{3}})

Solution steps

12 lo g_{7} (x) - 3 lo g_{7} (y)

Apply log rule:

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

12 lo g_{7} (x) = lo g_{7} (x^{12})

= lo g_{7} (x^{12}) - 3 lo g_{7} (y)

Apply log rule:

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

3 lo g_{7} (y) = lo g_{7} (y^{3})

= lo g_{7} (x^{12}) - lo g_{7} (y^{3})

Apply log rule:

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

lo g_{7} (x^{12}) - lo g_{7} (y^{3}) = lo g_{7} (\frac{x ^{12}}{y ^{3}})

= lo g_{7} (\frac{x ^{12}}{y ^{3}})

6 + 3 ln (\frac{1}{2})

lo g_{2} (\frac{c d ^{3}}{e ^{4}})

lo g_{10} (8^{2}) - lo g_{10} (12 5^{2})

lo g_{10} (3 (x + 1)^{2})

ln (x) - ln (x + 1)

What is 12log_{7}(x)-3log_{7}(y) ?
The solution to 12log_{7}(x)-3log_{7}(y) is log_{7}((x^{12})/(y^3))