What is 3log_{4}(x)+5log_{4}(y) ?

The solution to 3log_{4}(x)+5log_{4}(y) is log_{4}(x^3y^5)

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simplify 3log_{4}(x)+5log_{4}(y)

simplify

3 lo g_{4} (x) + 5 lo g_{4} (y)

lo g_{4} (x^{3} y^{5})

Solution steps

3 lo g_{4} (x) + 5 lo g_{4} (y)

Apply log rule:

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

3 lo g_{4} (x) = lo g_{4} (x^{3})

= lo g_{4} (x^{3}) + 5 lo g_{4} (y)

Apply log rule:

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

5 lo g_{4} (y) = lo g_{4} (y^{5})

= lo g_{4} (x^{3}) + lo g_{4} (y^{5})

Apply log rule:

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

lo g_{4} (x^{3}) + lo g_{4} (y^{5}) = lo g_{4} (x^{3} y^{5})

= lo g_{4} (x^{3} y^{5})

- \frac{4}{ln ( 6 ) 5}

\frac{3}{4} \cdot ln (2)

\frac{ln ( 2 ) - ln ( 2 - y )}{2}

ln (284.7) - ln (1002.5)

ln (\frac{30}{3.67})

What is 3log_{4}(x)+5log_{4}(y) ?
The solution to 3log_{4}(x)+5log_{4}(y) is log_{4}(x^3y^5)