What is 3log_{7}(x)+1/3 log_{7}(y) ?

The solution to 3log_{7}(x)+1/3 log_{7}(y) is log_{7}(x^3y^{1/3})

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simplify 3log_{7}(x)+1/3 log_{7}(y)

simplify

3 lo g_{7} (x) + \frac{1}{3} lo g_{7} (y)

lo g_{7} (x^{3} y^{\frac{1}{3}})

Solution steps

3 lo g_{7} (x) + \frac{1}{3} lo g_{7} (y)

Apply log rule:

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

3 lo g_{7} (x) = lo g_{7} (x^{3})

= lo g_{7} (x^{3}) + \frac{1}{3} lo g_{7} (y)

Apply log rule:

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

\frac{1}{3} lo g_{7} (y) = lo g_{7} (y^{\frac{1}{3}})

= lo g_{7} (x^{3}) + lo g_{7} (y^{\frac{1}{3}})

Apply log rule:

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

lo g_{7} (x^{3}) + lo g_{7} (y^{\frac{1}{3}}) = lo g_{7} (x^{3} y^{\frac{1}{3}})

= lo g_{7} (x^{3} y^{\frac{1}{3}})

- lo g_{10} (3.4 \cdot 1 0^{- 2})

- lo g_{10} (4.8 \cdot 1 0^{- 10} M)

ln (θ x^{(- x - θ)})

2 \cdot ln ∣ x - 1 ∣ + 5 \cdot ln ∣ x + 4 ∣ + C

3 + ln ((\frac{3}{2})^{- 3}) - 3 + ln (2^{2})

What is 3log_{7}(x)+1/3 log_{7}(y) ?
The solution to 3log_{7}(x)+1/3 log_{7}(y) is log_{7}(x^3y^{1/3})