Rewrite as sums or differences of logarithms.
$\ln \left(x^{5} y^{4} z\right)$
$\ln \left(x^{5} y^{4} z\right)=\square$

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Answer

Final Answer: $ \boxed{5 \ln x+4 \ln y+\ln z} $

Steps

Step 1 ：The given expression is a natural logarithm of a product of powers. According to the properties of logarithms, the logarithm of a product is the sum of the logarithms of the individual factors.

Step 2 ：Also, the logarithm of a power is the product of the exponent and the logarithm of the base.

Step 3 ：Therefore, we can rewrite the given expression as the sum of the logarithms of x, y, and z, each multiplied by their respective exponents.

Step 4 ：Final Answer: $ \boxed{5 \ln x+4 \ln y+\ln z} $

Rewrite as sums or differences of logarithms.$\ln \left(x^{5} y^{4} z\right)$$\ln \left(x^{5} y^{4} z\right)=\square$

Answer

Popular Problems

Rewrite as sums or differences of logarithms.
$\ln \left(x^{5} y^{4} z\right)$
$\ln \left(x^{5} y^{4} z\right)=\square$