Use the properties of logarithms to condense $6 \log _ { 10 } ( x + y ) + 4 \log _ { 10 } w$ .
A) $\log _ { 10 } x ^ { 6 } y ^ { 6 } w ^ { 4 }$
B) $\log _ { 10 } \left( x ^ { 6 } + y ^ { 6 } \right) w ^ { 4 }$
C) $\log _ { 10 } ( 6 ( x + y ) + 4 w )$
D) $\log _ { 10 } 24 ( x + y ) w$
E) $\log _ { 10 } ( x + y ) ^ { 6 } w ^ { 4 }$

Question

Quizplus · Accepted Answer

Using the property that states that the sum of logarithms is equivalent to the logarithm of the product, we can rewrite the expression as:

$$6 \log_{10}(x+y) + 4 \log_{10}w = \log_{10}(x+y)^6 + \log_{10}w^4 $$

Then, using the property that states that the logarithm of a product is equivalent to the sum of logarithms, we can condense the expression as:

$$\log_{10}(x+y)^6 + \log_{10}w^4 = \log_{10}(x+y)^6w^4$$

This matches answer choice E, so the best choice is E.

Use the Properties of Logarithms to Condense 6log⁡10(x+y)+4log⁡10w6 \log _ { 10 } ( x + y ) + 4 \log _ { 10 } w6log10​(x+y)+4log10​w

Use the Properties of Logarithms to Condense $6 \log _ { 10 } ( x + y ) + 4 \log _ { 10 } w$