What is log_{10}(((y^{5/3}))/(x^3*z^4)) ?

The solution to log_{10}(((y^{5/3}))/(x^3*z^4)) is 5/3 log_{10}(y)-3log_{10}(x)-4log_{10}(z)

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simplify log_{10}(((y^{5/3}))/(x^3*z^4))

simplify

lo g_{10} \frac{( y ^{\frac{5}{3}} )}{x ^{3} \cdot z ^{4}}

\frac{5}{3} lo g_{10} (y) - 3 lo g_{10} (x) - 4 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{y ^{\frac{5}{3}}}{x ^{3} z ^{4}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{y ^{\frac{5}{3}}}{x ^{3} z ^{4}}) = lo g_{10} (y^{\frac{5}{3}}) - lo g_{10} (x^{3} z^{4})

= lo g_{10} (y^{\frac{5}{3}}) - lo g_{10} (x^{3} z^{4})

lo g_{10} (y^{\frac{5}{3}}) = \frac{5}{3} lo g_{10} (y)

lo g_{10} (x^{3} z^{4}) = 3 lo g_{10} (x) + 4 lo g_{10} (z)

= \frac{5}{3} lo g_{10} (y) - (3 lo g_{10} (x) + 4 lo g_{10} (z))

Apply the distributive law:

- (a + b) = - a - b

- (3 lo g_{10} (x) + 4 lo g_{10} (z)) = - 3 lo g_{10} (x) - 4 lo g_{10} (z)

= \frac{5}{3} lo g_{10} (y) - 3 lo g_{10} (x) - 4 lo g_{10} (z)

lo g_{10} (10 \frac{10 x ^{100}}{10})

lo g_{a} (x^{3} y^{2})

\frac{ln ( 3 ) - ln ( 7 )}{2 ln ( 7 )}

\frac{( lo g _{3} ( 106 ) - lo g _{3} ( 5 ) )}{lo g _{3} ( 8 )}

ln (a) + ln (b) + ln (c)

What is log_{10}(((y^{5/3}))/(x^3*z^4)) ?
The solution to log_{10}(((y^{5/3}))/(x^3*z^4)) is 5/3 log_{10}(y)-3log_{10}(x)-4log_{10}(z)