What is 7log_{b}(x)-1/2 log_{b}(y)+3log_{b}(3) ?

The solution to 7log_{b}(x)-1/2 log_{b}(y)+3log_{b}(3) is log_{b}((27x^7sqrt(y))/y)

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simplify 7log_{b}(x)-1/2 log_{b}(y)+3log_{b}(3)

simplify

7 lo g_{b} (x) - \frac{1}{2} lo g_{b} (y) + 3 lo g_{b} (3)

lo g_{b} (\frac{27 x ^{7} y}{y})

Solution steps

7 lo g_{b} (x) - \frac{1}{2} lo g_{b} (y) + 3 lo g_{b} (3)

Apply log rule:

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

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

= lo g_{b} (x^{7}) - \frac{1}{2} lo g_{b} (y) + 3 lo g_{b} (3)

Apply log rule:

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

\frac{1}{2} lo g_{b} (y) = lo g_{b} (y^{\frac{1}{2}})

= lo g_{b} (x^{7}) - lo g_{b} (y^{\frac{1}{2}}) + 3 lo g_{b} (3)

Apply log rule:

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

lo g_{b} (x^{7}) - lo g_{b} (y^{\frac{1}{2}}) = lo g_{b} (\frac{x ^{7}}{y ^{\frac{1}{2}}})

= lo g_{b} (\frac{x ^{7}}{y ^{\frac{1}{2}}}) + 3 lo g_{b} (3)

Simplify

\frac{x ^{7}}{y ^{\frac{1}{2}}} : \frac{x ^{7} y}{y}

= lo g_{b} (\frac{x ^{7} y}{y}) + 3 lo g_{b} (3)

Apply log rule:

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

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

= lo g_{b} (\frac{x ^{7} y}{y}) + lo g_{b} (3^{3})

Apply log rule:

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

lo g_{b} (\frac{x ^{7} y}{y}) + lo g_{b} (3^{3}) = lo g_{b} (3^{3} \cdot \frac{x ^{7} y}{y})

= lo g_{b} (3^{3} \cdot \frac{x ^{7} y}{y})

Simplify

\frac{x ^{7} y}{y} \cdot 3^{3} : \frac{27 x ^{7} y}{y}

= lo g_{b} (\frac{27 x ^{7} y}{y})

ln (9 \cdot e^{- 3 t})

- lo g_{10} (3.26 \cdot 1 0^{- 2})

6 ln (x + 8) - 9 ln (x)

\frac{5}{3} ln ∣ 5 ∣ - \frac{2}{3} ln ∣ 2 ∣

lo g_{3} (\frac{1}{25 \cdot 3 \cdot 5})

What is 7log_{b}(x)-1/2 log_{b}(y)+3log_{b}(3) ?
The solution to 7log_{b}(x)-1/2 log_{b}(y)+3log_{b}(3) is log_{b}((27x^7sqrt(y))/y)