What is 7log_{b}(w)-1/5 log_{b}(y)+3log_{b}(x) ?

The solution to 7log_{b}(w)-1/5 log_{b}(y)+3log_{b}(x) is log_{b}((w^7x^3y^{4/5})/y)

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simplify 7log_{b}(w)-1/5 log_{b}(y)+3log_{b}(x)

simplify

7 lo g_{b} (w) - \frac{1}{5} lo g_{b} (y) + 3 lo g_{b} (x)

lo g_{b} (\frac{w ^{7} x ^{3} y ^{\frac{4}{5}}}{y})

Solution steps

7 lo g_{b} (w) - \frac{1}{5} lo g_{b} (y) + 3 lo g_{b} (x)

Apply log rule:

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

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

= lo g_{b} (w^{7}) - \frac{1}{5} lo g_{b} (y) + 3 lo g_{b} (x)

Apply log rule:

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

\frac{1}{5} lo g_{b} (y) = lo g_{b} (y^{\frac{1}{5}})

= lo g_{b} (w^{7}) - lo g_{b} (y^{\frac{1}{5}}) + 3 lo g_{b} (x)

Apply log rule:

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

lo g_{b} (w^{7}) - lo g_{b} (y^{\frac{1}{5}}) = lo g_{b} (\frac{w ^{7}}{y ^{\frac{1}{5}}})

= lo g_{b} (\frac{w ^{7}}{y ^{\frac{1}{5}}}) + 3 lo g_{b} (x)

Simplify

\frac{w ^{7}}{y ^{\frac{1}{5}}} : \frac{w ^{7} y ^{\frac{4}{5}}}{y}

= lo g_{b} (\frac{w ^{7} y ^{\frac{4}{5}}}{y}) + 3 lo g_{b} (x)

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} (\frac{w ^{7} y ^{\frac{4}{5}}}{y}) + lo g_{b} (x^{3})

Apply log rule:

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

lo g_{b} (\frac{w ^{7} y ^{\frac{4}{5}}}{y}) + lo g_{b} (x^{3}) = lo g_{b} (\frac{w ^{7} y ^{\frac{4}{5}}}{y} x^{3})

= lo g_{b} (\frac{w ^{7} y ^{\frac{4}{5}}}{y} x^{3})

Simplify

\frac{w ^{7} y ^{\frac{4}{5}}}{y} x^{3} : \frac{w ^{7} x ^{3} y ^{\frac{4}{5}}}{y}

= lo g_{b} (\frac{w ^{7} x ^{3} y ^{\frac{4}{5}}}{y})

- lo g_{10} (1.1004 \cdot 1 0^{- 10})

3.86 + lo g_{10} (\frac{0.004}{0.021})

ln (a X^{b} Y^{c})

\frac{1}{2} ln ∣ 2 (9) + 1 ∣ + 2 ln ∣ 9 - 1 ∣

ln (\frac{1643.85}{547.85}) \cdot 8

What is 7log_{b}(w)-1/5 log_{b}(y)+3log_{b}(x) ?
The solution to 7log_{b}(w)-1/5 log_{b}(y)+3log_{b}(x) is log_{b}((w^7x^3y^{4/5})/y)