What is 3log_{10}(x)+2log_{10}(z) ?

The solution to 3log_{10}(x)+2log_{10}(z) is log_{10}(x^3z^2)

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simplify 3log_{10}(x)+2log_{10}(z)

simplify

3 lo g_{10} (x) + 2 lo g_{10} (z)

lo g_{10} (x^{3} z^{2})

Solution steps

3 lo g_{10} (x) + 2 lo g_{10} (z)

Apply log rule:

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

3 lo g_{10} (x) = lo g_{10} (x^{3})

= lo g_{10} (x^{3}) + 2 lo g_{10} (z)

Apply log rule:

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

2 lo g_{10} (z) = lo g_{10} (z^{2})

= lo g_{10} (x^{3}) + lo g_{10} (z^{2})

Apply log rule:

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

lo g_{10} (x^{3}) + lo g_{10} (z^{2}) = lo g_{10} (x^{3} z^{2})

= lo g_{10} (x^{3} z^{2})

ln (\frac{1}{2 - 3})

ln (e^{- y} \cdot y^{x})

- 8 ln (\frac{1}{2}) + 4

\frac{1}{7} ln (2)

2 ln (5) + ln (10) - \frac{1}{2} ln (4)

What is 3log_{10}(x)+2log_{10}(z) ?
The solution to 3log_{10}(x)+2log_{10}(z) is log_{10}(x^3z^2)