What is ln((sqrt(x))/(y^2z^2)) ?

The solution to ln((sqrt(x))/(y^2z^2)) is ln(sqrt(x))-2ln(y)-2ln(z)

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simplify ln((sqrt(x))/(y^2z^2))

simplify

ln (\frac{x}{y ^{2} z ^{2}})

ln (x) - 2 ln (y) - 2 ln (z)

Solution steps

ln (\frac{x}{y ^{2} z ^{2}})

Apply log rule:

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

ln (\frac{x}{y ^{2} z ^{2}}) = ln (x) - ln (y^{2} z^{2})

= ln (x) - ln (y^{2} z^{2})

Apply log rule:

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

ln (y^{2} z^{2}) = ln (y^{2}) + ln (z^{2})

= ln (x) - (ln (y^{2}) + ln (z^{2}))

Apply log rule:

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

ln (y^{2}) = 2 ln (y)

= ln (x) - (2 ln (y) + ln (z^{2}))

Apply log rule:

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

ln (z^{2}) = 2 ln (z)

= ln (x) - (2 ln (y) + 2 ln (z))

- (2 ln (y) + 2 ln (z)) : - 2 ln (y) - 2 ln (z)

= ln (x) - 2 ln (y) - 2 ln (z)

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

lo g_{10} (\frac{y}{x}) e^{4}

- lo g_{10} (1.2 \cdot 1 0^{- 6})

ln (8.2) - ln (7.5)

ln (0.69 \cdot 1 0^{3})

What is ln((sqrt(x))/(y^2z^2)) ?
The solution to ln((sqrt(x))/(y^2z^2)) is ln(sqrt(x))-2ln(y)-2ln(z)