What is 2log_{5}(x)+12log_{5}(y) ?

The solution to 2log_{5}(x)+12log_{5}(y) is log_{5}(x^2y^{12})

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simplify 2log_{5}(x)+12log_{5}(y)

simplify

2 lo g_{5} (x) + 12 lo g_{5} (y)

lo g_{5} (x^{2} y^{12})

Solution steps

2 lo g_{5} (x) + 12 lo g_{5} (y)

Apply log rule:

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

2 lo g_{5} (x) = lo g_{5} (x^{2})

= lo g_{5} (x^{2}) + 12 lo g_{5} (y)

Apply log rule:

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

12 lo g_{5} (y) = lo g_{5} (y^{12})

= lo g_{5} (x^{2}) + lo g_{5} (y^{12})

Apply log rule:

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

lo g_{5} (x^{2}) + lo g_{5} (y^{12}) = lo g_{5} (x^{2} y^{12})

= lo g_{5} (x^{2} y^{12})

3 ln (x) + 6 ln (y) - 2 ln (z)

4 lo g_{b} (x) + 6 lo g_{b} (z)

lo g_{10} (\frac{x ^{2}}{y ^{4}})

lo g_{10} (2) - lo g_{10} (5)

lo g_{10} (\frac{ab}{c d})

What is 2log_{5}(x)+12log_{5}(y) ?
The solution to 2log_{5}(x)+12log_{5}(y) is log_{5}(x^2y^{12})