What is 6log_{b}(x)+1/3 log_{b}(y) ?

The solution to 6log_{b}(x)+1/3 log_{b}(y) is log_{b}(x^6y^{1/3})

Popular >

simplify 6log_{b}(x)+1/3 log_{b}(y)

simplify

6 lo g_{b} (x) + \frac{1}{3} lo g_{b} (y)

lo g_{b} (x^{6} y^{\frac{1}{3}})

Solution steps

6 lo g_{b} (x) + \frac{1}{3} lo g_{b} (y)

Apply log rule:

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

6 lo g_{b} (x) = lo g_{b} (x^{6})

= lo g_{b} (x^{6}) + \frac{1}{3} lo g_{b} (y)

Apply log rule:

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

\frac{1}{3} lo g_{b} (y) = lo g_{b} (y^{\frac{1}{3}})

= lo g_{b} (x^{6}) + lo g_{b} (y^{\frac{1}{3}})

Apply log rule:

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

lo g_{b} (x^{6}) + lo g_{b} (y^{\frac{1}{3}}) = lo g_{b} (x^{6} y^{\frac{1}{3}})

= lo g_{b} (x^{6} y^{\frac{1}{3}})

3 ln (y) + ln (x)

lo g_{a} (b x)

lo g_{10} (3) - 2 lo g_{10} (5)

lo g_{10} (\frac{10 z}{8})

lo g_{11} ((x + y) \cdot z)

What is 6log_{b}(x)+1/3 log_{b}(y) ?
The solution to 6log_{b}(x)+1/3 log_{b}(y) is log_{b}(x^6y^{1/3})