What is 2log_{b}(x)-3log_{b}(y)+4log_{b}(z) ?

The solution to 2log_{b}(x)-3log_{b}(y)+4log_{b}(z) is log_{b}((x^2z^4)/(y^3))

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simplify 2log_{b}(x)-3log_{b}(y)+4log_{b}(z)

simplify

2 lo g_{b} (x) - 3 lo g_{b} (y) + 4 lo g_{b} (z)

lo g_{b} (\frac{x ^{2} z ^{4}}{y ^{3}})

Solution steps

2 lo g_{b} (x) - 3 lo g_{b} (y) + 4 lo g_{b} (z)

Apply log rule:

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

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

= lo g_{b} (x^{2}) - 3 lo g_{b} (y) + 4 lo g_{b} (z)

Apply log rule:

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

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

= lo g_{b} (x^{2}) - lo g_{b} (y^{3}) + 4 lo g_{b} (z)

Apply log rule:

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

lo g_{b} (x^{2}) - lo g_{b} (y^{3}) = lo g_{b} (\frac{x ^{2}}{y ^{3}})

= lo g_{b} (\frac{x ^{2}}{y ^{3}}) + 4 lo g_{b} (z)

Apply log rule:

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

4 lo g_{b} (z) = lo g_{b} (z^{4})

= lo g_{b} (\frac{x ^{2}}{y ^{3}}) + lo g_{b} (z^{4})

Apply log rule:

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

lo g_{b} (\frac{x ^{2}}{y ^{3}}) + lo g_{b} (z^{4}) = lo g_{b} (\frac{x ^{2}}{y ^{3}} z^{4})

= lo g_{b} (\frac{x ^{2}}{y ^{3}} z^{4})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= lo g_{b} (\frac{x ^{2} z ^{4}}{y ^{3}})

\frac{3}{2} ln (x^{10}) - \frac{4}{5} ln (2 y^{10})

- lo g_{10} (4.3 \cdot 1 0^{- 11})

ln (\frac{1 n}{1})

ln (5 \cdot 1 0^{- 4})

- lo g_{10} (7.56 \cdot 1 0^{6})

What is 2log_{b}(x)-3log_{b}(y)+4log_{b}(z) ?
The solution to 2log_{b}(x)-3log_{b}(y)+4log_{b}(z) is log_{b}((x^2z^4)/(y^3))