What is 5log_{3}(x)+2/3 log_{3}(y) ?

The solution to 5log_{3}(x)+2/3 log_{3}(y) is log_{3}(x^5y^{2/3})

Popular >

simplify 5log_{3}(x)+2/3 log_{3}(y)

simplify

5 lo g_{3} (x) + \frac{2}{3} lo g_{3} (y)

lo g_{3} (x^{5} y^{\frac{2}{3}})

Solution steps

5 lo g_{3} (x) + \frac{2}{3} lo g_{3} (y)

Apply log rule:

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

5 lo g_{3} (x) = lo g_{3} (x^{5})

= lo g_{3} (x^{5}) + \frac{2}{3} lo g_{3} (y)

Apply log rule:

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

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

= lo g_{3} (x^{5}) + lo g_{3} (y^{\frac{2}{3}})

Apply log rule:

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

lo g_{3} (x^{5}) + lo g_{3} (y^{\frac{2}{3}}) = lo g_{3} (x^{5} y^{\frac{2}{3}})

= lo g_{3} (x^{5} y^{\frac{2}{3}})

ln (\frac{x ( x ^{2} + 1 )}{x ^{2} + 1})

\frac{15 ln ( \frac{5}{21} )}{ln ( \frac{13}{21} )}

ln (\frac{70}{50}) + (\frac{1}{2} \cdot 0. 4^{2}) \cdot 4

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

- ln (5) - ln (7) + ln (3)

What is 5log_{3}(x)+2/3 log_{3}(y) ?
The solution to 5log_{3}(x)+2/3 log_{3}(y) is log_{3}(x^5y^{2/3})