What is (ne)/(ln(x)+2ln(y)-(1/2)ln(z)) ?

The solution to (ne)/(ln(x)+2ln(y)-(1/2)ln(z)) is (ne}{ln(\frac{xy^2sqrt(z))/z)}

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simplify (ne)/(ln(x)+2ln(y)-(1/2)ln(z))

simplify

\frac{n e}{ln ( x ) + 2 ln ( y ) - ( \frac{1}{2} ) ln ( z )}

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

Solution steps

\frac{n e}{ln ( x ) + 2 ln ( y ) - ( \frac{1}{2} ) ln ( z )}

Apply log rule:

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

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

= \frac{e n}{ln ( x ) + ln ( y ^{2} ) - ( \frac{1}{2} ) ln ( z )}

Apply log rule:

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

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

= \frac{n e}{ln ( x y ^{2} ) - \frac{1}{2} ln ( z )}

Apply log rule:

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

\frac{1}{2} ln (z) = ln (z^{\frac{1}{2}})

= \frac{e n}{ln ( x y ^{2} ) - ln ( z ^{\frac{1}{2}} )}

Apply log rule:

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

ln (x y^{2}) - ln (z^{\frac{1}{2}}) = ln (\frac{x y ^{2}}{z ^{\frac{1}{2}}})

= \frac{e n}{ln ( \frac{x y ^{2}}{z ^{\frac{1}{2}}} )}

Simplify

\frac{x y ^{2}}{z ^{\frac{1}{2}}} : \frac{x y ^{2} z}{z}

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

lo g_{10} (x) 7 - lo g_{10} (5)

0.462 - \frac{0.0592}{2} lo g_{10} (\frac{0.2}{0.01})

\frac{1}{2} (0.375983) + \frac{1}{4} (ln (1.25) + ln (1.75))

ln (\frac{547.85}{273.85}) \cdot 8

ln (27500) - ln (22617)

What is (ne)/(ln(x)+2ln(y)-(1/2)ln(z)) ?
The solution to (ne)/(ln(x)+2ln(y)-(1/2)ln(z)) is (ne}{ln(\frac{xy^2sqrt(z))/z)}