What is 3log_{b}(x)+6log_{b}(z) ?

The solution to 3log_{b}(x)+6log_{b}(z) is log_{b}(x^3z^6)

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simplify 3log_{b}(x)+6log_{b}(z)

simplify

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

lo g_{b} (x^{3} z^{6})

Solution steps

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

Apply log rule:

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

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

= lo g_{b} (x^{3}) + 6 lo g_{b} (z)

Apply log rule:

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

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

= lo g_{b} (x^{3}) + lo g_{b} (z^{6})

Apply log rule:

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

lo g_{b} (x^{3}) + lo g_{b} (z^{6}) = lo g_{b} (x^{3} z^{6})

= lo g_{b} (x^{3} z^{6})

- lo g_{10} (4.5 \cdot 1 0^{- 5})

ln (125) - 2 ln (5)

- lo g_{10} (5 \cdot 1 0^{- 11})

\frac{ln ( 2 + 0.00005 ) - ln ( 2 )}{0.00005}

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

What is 3log_{b}(x)+6log_{b}(z) ?
The solution to 3log_{b}(x)+6log_{b}(z) is log_{b}(x^3z^6)