What is expand log_{7}((x^3sqrt(y))/(18)) ?

The solution to expand log_{7}((x^3sqrt(y))/(18)) is 3log_{7}(x)+log_{7}(sqrt(y))-log_{7}(18)

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expand log_{7}((x^3sqrt(y))/(18))

expand

lo g_{7} (\frac{x ^{3} y}{18})

3 lo g_{7} (x) + lo g_{7} (y) - lo g_{7} (18)

Solution steps

lo g_{7} (\frac{x ^{3} y}{18})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{7} (\frac{x ^{3} y}{18}) = lo g_{7} (x^{3} y) - lo g_{7} (18)

= lo g_{7} (x^{3} y) - lo g_{7} (18)

Apply log rule:

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

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

= lo g_{7} (x^{3}) + lo g_{7} (y) - lo g_{7} (18)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 3 lo g_{7} (x) + lo g_{7} (y) - lo g_{7} (18)

ln (x) + ln (15)

ln (\frac{2 + 1}{2 - 1})

lo g_{10} (x)

\frac{3}{2} lo g_{2} (x - y) - 2 lo g_{2} (x^{2} + y^{2})

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

What is expand log_{7}((x^3sqrt(y))/(18)) ?
The solution to expand log_{7}((x^3sqrt(y))/(18)) is 3log_{7}(x)+log_{7}(sqrt(y))-log_{7}(18)