What is 7log_{5}(a)+4log_{5}(z) ?

The solution to 7log_{5}(a)+4log_{5}(z) is log_{5}(a^7z^4)

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simplify 7log_{5}(a)+4log_{5}(z)

simplify

7 lo g_{5} (a) + 4 lo g_{5} (z)

lo g_{5} (a^{7} z^{4})

Solution steps

7 lo g_{5} (a) + 4 lo g_{5} (z)

Apply log rule:

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

7 lo g_{5} (a) = lo g_{5} (a^{7})

= lo g_{5} (a^{7}) + 4 lo g_{5} (z)

Apply log rule:

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

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

= lo g_{5} (a^{7}) + lo g_{5} (z^{4})

Apply log rule:

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

lo g_{5} (a^{7}) + lo g_{5} (z^{4}) = lo g_{5} (a^{7} z^{4})

= lo g_{5} (a^{7} z^{4})

ln (x^{2} + 3 x + 3) - ln (x^{2} + x + 1)

ln (\frac{3 \cdot x ^{3} + 2 \cdot π}{9 \cdot x + c})

- ln ∣ p ∣ + ln ∣ p - 3 ∣

ln (x^{3} \cdot y z)

ln ∣ x - 2 ∣ - ln ∣ x - 1 ∣

What is 7log_{5}(a)+4log_{5}(z) ?
The solution to 7log_{5}(a)+4log_{5}(z) is log_{5}(a^7z^4)