Question 7 of 10

Write the following expression as a sum and/or difference of logarithms. Express powers as factors.
$\log_{c} (u^{3} v^{8}) u > 0, v > 0$
$\log_{c} (u^{3} v^{8}) = ◻ ($ Simplify your answer. $)$

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Answer

$\log_{c} (u^{3} v^{8}) = 3 \log_{c} (u) + 8 \log_{c} (v)$

Steps

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

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

Step 3 ：Therefore, we can rewrite the given expression as a sum of logarithms, where the powers are expressed as factors.

Step 4 ： $\log_{c} (u^{3} v^{8}) = 3 \log_{c} (u) + 8 \log_{c} (v)$

Step 5 ： $\log_{c} (u^{3} v^{8}) = 3 \log_{c} (u) + 8 \log_{c} (v)$

Question 7 of 10 Write the following expression as a sum and/or difference of logarithms. Express powers as factors.logc⁡(u3v8)u>0,v>0logc⁡(u3v8)=◻( Simplify your answer. )

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Question 7 of 10

Write the following expression as a sum and/or difference of logarithms. Express powers as factors.
$\log_{c} (u^{3} v^{8}) u > 0, v > 0$
$\log_{c} (u^{3} v^{8}) = ◻ ($ Simplify your answer. $)$