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Popular >

simplify ln(X)+ln(Y)-3ln(Z)

Solution

simplify

ln (X) + ln (Y) - 3 ln (Z)

Solution

ln (\frac{X Y}{Z ^{3}})

Solution steps

ln (X) + ln (Y) - 3 ln (Z)

Apply log rule:

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

ln (X) + ln (Y) = ln (X Y)

= ln (X Y) - 3 ln (Z)

Apply log rule:

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

3 ln (Z) = ln (Z^{3})

= ln (X Y) - ln (Z^{3})

Apply log rule:

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

ln (X Y) - ln (Z^{3}) = ln (\frac{X Y}{Z ^{3}})

= ln (\frac{X Y}{Z ^{3}})

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Frequently Asked Questions (FAQ)

What is ln(X)+ln(Y)-3ln(Z) ?
The solution to ln(X)+ln(Y)-3ln(Z) is ln((XY)/(Z^3))