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Popular >

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

Solution

simplify

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

Solution

ln (\frac{x y}{z ^{5}})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (x y) - ln (z^{5}) = ln (\frac{x y}{z ^{5}})

= ln (\frac{x y}{z ^{5}})

Popular Examples

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lo g_{10} (7 x^{4})

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7 lo g_{a} (m) - \frac{1}{3} lo g_{a} (r)

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ln (\frac{29}{22.6})

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4 \cdot lo g_{10} (43488 3 \cdot 1 0^{- 2}) - 4

Frequently Asked Questions (FAQ)

What is ln(x)+ln(y)-5ln(z) ?
The solution to ln(x)+ln(y)-5ln(z) is ln((xy)/(z^5))