What is 5log_{3}(z)+7log_{3}(y) ?

The solution to 5log_{3}(z)+7log_{3}(y) is log_{3}(z^5y^7)

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simplify 5log_{3}(z)+7log_{3}(y)

simplify

5 lo g_{3} (z) + 7 lo g_{3} (y)

lo g_{3} (z^{5} y^{7})

Solution steps

5 lo g_{3} (z) + 7 lo g_{3} (y)

Apply log rule:

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

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

= lo g_{3} (z^{5}) + 7 lo g_{3} (y)

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} (z^{5}) + lo g_{3} (y^{7})

Apply log rule:

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

lo g_{3} (z^{5}) + lo g_{3} (y^{7}) = lo g_{3} (z^{5} y^{7})

= lo g_{3} (z^{5} y^{7})

1.76776 ln (\frac{1}{( 2 2 )})

0.8 + 1.4 \cdot ln (\frac{π \cdot 10 0 ^{2}}{1200})

ln (16 \cdot 1 0^{3})

ln (\frac{233955}{388533}) - ln (1 - \frac{233955}{388533})

(1.3)^{2} + ln (\frac{1}{1.3}) - ln (2 e^{1})

What is 5log_{3}(z)+7log_{3}(y) ?
The solution to 5log_{3}(z)+7log_{3}(y) is log_{3}(z^5y^7)