What is 6log_{b}(x)+7log_{b}(z) ?

The solution to 6log_{b}(x)+7log_{b}(z) is log_{b}(x^6z^7)

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simplify 6log_{b}(x)+7log_{b}(z)

simplify

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

lo g_{b} (x^{6} z^{7})

Solution steps

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

Apply log rule:

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

6 lo g_{b} (x) = lo g_{b} (x^{6})

= lo g_{b} (x^{6}) + 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} (x^{6}) + lo g_{b} (z^{7})

Apply log rule:

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

lo g_{b} (x^{6}) + lo g_{b} (z^{7}) = lo g_{b} (x^{6} z^{7})

= lo g_{b} (x^{6} z^{7})

lo g_{2} (\frac{a - 1}{9})

lo g_{10} (2 π)

3.3 + lo g_{10} (\frac{0.3 - 0.05}{0.25 + 0.05})

- lo g_{10} (1.5 \cdot 1 0^{- 4})

- 0.4 lo g_{2} (0.4) - 0.6 lo g_{2} (0.6)

What is 6log_{b}(x)+7log_{b}(z) ?
The solution to 6log_{b}(x)+7log_{b}(z) is log_{b}(x^6z^7)