What is expand log_{5}((sqrt(x))/(3^2z)) ?

The solution to expand log_{5}((sqrt(x))/(3^2z)) is log_{5}(sqrt(x))-2log_{5}(3)-log_{5}(z)

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expand log_{5}((sqrt(x))/(3^2z))

expand

lo g_{5} (\frac{x}{3 ^{2} z})

lo g_{5} (x) - 2 lo g_{5} (3) - lo g_{5} (z)

Solution steps

lo g_{5} (\frac{x}{3 ^{2} z})

Apply log rule:

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

lo g_{5} (\frac{x}{3 ^{2} z}) = lo g_{5} (x) - lo g_{5} (3^{2} z)

= lo g_{5} (x) - lo g_{5} (3^{2} z)

Apply log rule:

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

lo g_{5} (3^{2} z) = lo g_{5} (3^{2}) + lo g_{5} (z)

= lo g_{5} (x) - (lo g_{5} (z) + lo g_{5} (3^{2}))

Apply log rule:

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

lo g_{5} (3^{2}) = 2 lo g_{5} (3)

= lo g_{5} (x) - (2 lo g_{5} (3) + lo g_{5} (z))

- (2 lo g_{5} (3) + lo g_{5} (z)) : - 2 lo g_{5} (3) - lo g_{5} (z)

= lo g_{5} (x) - 2 lo g_{5} (3) - lo g_{5} (z)

ln (e^{3 x}) + ln (x^{3}) - ln (3 x)

ln (25 e^{2} \cdot \frac{1}{36})

ln (x^{4}) - ln (x)

lo g_{5} (4) - lo g_{5} (9)

lo g_{m} (\frac{67}{83})

What is expand log_{5}((sqrt(x))/(3^2z)) ?
The solution to expand log_{5}((sqrt(x))/(3^2z)) is log_{5}(sqrt(x))-2log_{5}(3)-log_{5}(z)