What is 5ln(x)+2ln(y)+ln(z) ?

The solution to 5ln(x)+2ln(y)+ln(z) is ln(x^5y^2z)

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simplify 5ln(x)+2ln(y)+ln(z)

simplify

5 ln (x) + 2 ln (y) + ln (z)

ln (x^{5} y^{2} z)

Solution steps

5 ln (x) + 2 ln (y) + ln (z)

Apply log rule:

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

5 ln (x) = ln (x^{5})

= ln (x^{5}) + 2 ln (y) + ln (z)

Apply log rule:

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

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

= ln (x^{5}) + ln (y^{2}) + ln (z)

Apply log rule:

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

ln (x^{5}) + ln (y^{2}) = ln (x^{5} y^{2})

= ln (x^{5} y^{2}) + ln (z)

Apply log rule:

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

ln (x^{5} y^{2}) + ln (z) = ln (x^{5} y^{2} z)

= ln (x^{5} y^{2} z)

ln (\frac{100}{10})

lo g_{4} (\frac{3 x ^{2}}{y ^{3}})

ln (\frac{( x y ^{4} )}{z ^{3}})

- lo g_{10} (1.5 \cdot 1 0^{- 7})

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

What is 5ln(x)+2ln(y)+ln(z) ?
The solution to 5ln(x)+2ln(y)+ln(z) is ln(x^5y^2z)