What is 7log_{b}(x)+5log_{b}(z) ?

The solution to 7log_{b}(x)+5log_{b}(z) is log_{b}(x^7z^5)

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simplify 7log_{b}(x)+5log_{b}(z)

simplify

7 lo g_{b} (x) + 5 lo g_{b} (z)

lo g_{b} (x^{7} z^{5})

Solution steps

7 lo g_{b} (x) + 5 lo g_{b} (z)

Apply log rule:

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

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

= lo g_{b} (x^{7}) + 5 lo g_{b} (z)

Apply log rule:

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

5 lo g_{b} (z) = lo g_{b} (z^{5})

= lo g_{b} (x^{7}) + lo g_{b} (z^{5})

Apply log rule:

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

lo g_{b} (x^{7}) + lo g_{b} (z^{5}) = lo g_{b} (x^{7} z^{5})

= lo g_{b} (x^{7} z^{5})

lo g_{a} (\frac{1}{2})

lo g_{4} (3) - lo g_{4} (t)

\frac{1}{2} lo g_{a} (x) + 3 lo g_{a} (y) - 3 lo g_{a} (x)

ln (12) - ln (3)

lo g_{10} (\frac{10 a \cdot 0.1}{10})

What is 7log_{b}(x)+5log_{b}(z) ?
The solution to 7log_{b}(x)+5log_{b}(z) is log_{b}(x^7z^5)