What is 7log_{3}(y)-1/4 log_{3}(z)+2log_{3}(x) ?

The solution to 7log_{3}(y)-1/4 log_{3}(z)+2log_{3}(x) is log_{3}((y^7x^2z^{3/4})/z)

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simplify 7log_{3}(y)-1/4 log_{3}(z)+2log_{3}(x)

simplify

7 lo g_{3} (y) - \frac{1}{4} lo g_{3} (z) + 2 lo g_{3} (x)

lo g_{3} (\frac{y ^{7} x ^{2} z ^{\frac{3}{4}}}{z})

Solution steps

7 lo g_{3} (y) - \frac{1}{4} lo g_{3} (z) + 2 lo g_{3} (x)

Apply log rule:

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

7 lo g_{3} (y) = lo g_{3} (y^{7})

= lo g_{3} (y^{7}) - \frac{1}{4} lo g_{3} (z) + 2 lo g_{3} (x)

Apply log rule:

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

\frac{1}{4} lo g_{3} (z) = lo g_{3} (z^{\frac{1}{4}})

= lo g_{3} (y^{7}) - lo g_{3} (z^{\frac{1}{4}}) + 2 lo g_{3} (x)

Apply log rule:

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

lo g_{3} (y^{7}) - lo g_{3} (z^{\frac{1}{4}}) = lo g_{3} (\frac{y ^{7}}{z ^{\frac{1}{4}}})

= lo g_{3} (\frac{y ^{7}}{z ^{\frac{1}{4}}}) + 2 lo g_{3} (x)

Simplify

\frac{y ^{7}}{z ^{\frac{1}{4}}} : \frac{y ^{7} z ^{\frac{3}{4}}}{z}

= lo g_{3} (\frac{y ^{7} z ^{\frac{3}{4}}}{z}) + 2 lo g_{3} (x)

Apply log rule:

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

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

= lo g_{3} (\frac{y ^{7} z ^{\frac{3}{4}}}{z}) + lo g_{3} (x^{2})

Apply log rule:

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

lo g_{3} (\frac{y ^{7} z ^{\frac{3}{4}}}{z}) + lo g_{3} (x^{2}) = lo g_{3} (\frac{y ^{7} z ^{\frac{3}{4}}}{z} x^{2})

= lo g_{3} (\frac{y ^{7} z ^{\frac{3}{4}}}{z} x^{2})

Simplify

\frac{y ^{7} z ^{\frac{3}{4}}}{z} x^{2} : \frac{y ^{7} x ^{2} z ^{\frac{3}{4}}}{z}

= lo g_{3} (\frac{y ^{7} x ^{2} z ^{\frac{3}{4}}}{z})

ln ∣ x + 2 ∣ - \frac{1}{2} ln y^{2} - 1

lo g_{10} (\frac{x ^{3} y}{z})

0.0296 \cdot 46 e^{(\frac{l n ( 263 ) - l n ( 46 )}{30}) 3}

- \frac{1}{2} ln ∣ v + 2 ∣ + \frac{1}{2} ln ∣ v ∣

ln (\frac{1}{a} e^{- \frac{y}{a}})

What is 7log_{3}(y)-1/4 log_{3}(z)+2log_{3}(x) ?
The solution to 7log_{3}(y)-1/4 log_{3}(z)+2log_{3}(x) is log_{3}((y^7x^2z^{3/4})/z)