What is 2log_{10}(x)-3log_{10}(z)+1 ?

The solution to 2log_{10}(x)-3log_{10}(z)+1 is log_{10}((x^2)/(z^3))+1

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simplify 2log_{10}(x)-3log_{10}(z)+1

simplify

2 lo g_{10} (x) - 3 lo g_{10} (z) + 1

lo g_{10} (\frac{x ^{2}}{z ^{3}}) + 1

Solution steps

2 lo g_{10} (x) - 3 lo g_{10} (z) + 1

Apply log rule:

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

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

= lo g_{10} (x^{2}) - 3 lo g_{10} (z) + 1

Apply log rule:

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

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

= lo g_{10} (x^{2}) - lo g_{10} (z^{3}) + 1

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

= lo g_{10} (\frac{x ^{2}}{z ^{3}}) + 1

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What is 2log_{10}(x)-3log_{10}(z)+1 ?
The solution to 2log_{10}(x)-3log_{10}(z)+1 is log_{10}((x^2)/(z^3))+1