What is 7log_{b}(x)+3log_{b}(z) ?

The solution to 7log_{b}(x)+3log_{b}(z) is log_{b}(x^7z^3)

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simplify 7log_{b}(x)+3log_{b}(z)

simplify

7 lo g_{b} (x) + 3 lo g_{b} (z)

lo g_{b} (x^{7} z^{3})

Solution steps

7 lo g_{b} (x) + 3 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}) + 3 lo g_{b} (z)

Apply log rule:

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

3 lo g_{b} (z) = lo g_{b} (z^{3})

= lo g_{b} (x^{7}) + lo g_{b} (z^{3})

Apply log rule:

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

lo g_{b} (x^{7}) + lo g_{b} (z^{3}) = lo g_{b} (x^{7} z^{3})

= lo g_{b} (x^{7} z^{3})

lo g_{10} (A) - lo g_{10} (B)

lo g_{10} (\frac{x ^{2} ( 1 + x ^{2} ) ^{2}}{( 1 - x ^{2} ) ^{2}})

lo g_{6} ((\frac{z}{36})^{4})

\frac{1}{2} lo g_{10} (16 x^{4}) + lo g_{10} (2 x)

lo g_{a} (26) + lo g_{a} (4)

What is 7log_{b}(x)+3log_{b}(z) ?
The solution to 7log_{b}(x)+3log_{b}(z) is log_{b}(x^7z^3)