What is 4log_{b}(y)+7log_{b}(z) ?

The solution to 4log_{b}(y)+7log_{b}(z) is log_{b}(y^4z^7)

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simplify 4log_{b}(y)+7log_{b}(z)

simplify

4 lo g_{b} (y) + 7 lo g_{b} (z)

lo g_{b} (y^{4} z^{7})

Solution steps

4 lo g_{b} (y) + 7 lo g_{b} (z)

Apply log rule:

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

4 lo g_{b} (y) = lo g_{b} (y^{4})

= lo g_{b} (y^{4}) + 7 lo g_{b} (z)

Apply log rule:

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

7 lo g_{b} (z) = lo g_{b} (z^{7})

= lo g_{b} (y^{4}) + lo g_{b} (z^{7})

Apply log rule:

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

lo g_{b} (y^{4}) + lo g_{b} (z^{7}) = lo g_{b} (y^{4} z^{7})

= lo g_{b} (y^{4} z^{7})

lo g_{7} (\frac{w ^{2}}{v})

lo g_{2} (3 x y)

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

ln (x) - ln (5 x)

What is 4log_{b}(y)+7log_{b}(z) ?
The solution to 4log_{b}(y)+7log_{b}(z) is log_{b}(y^4z^7)