Use the properties of logarithms to condense log ⁡ 7 x − log ⁡ 7 4 \log _ { 7 } x - \log _ { 7 } 4 lo g 7 x − lo g 7 4 .A) log ⁡ 7 ( x − 4 ) \log _ { 7 } ( x - 4 ) lo g 7 ( x − 4 ) B) log ⁡ 7 x 4 \log _ { 7 } \frac { x } { 4 } lo g 7 4 x C) ( log ⁡ 7 x ) 1 / 4 \left( \log _ { 7 } x \right) ^ { 1 / 4 } ( lo g 7 x ) 1/4 D) log ⁡ 7 x log ⁡ 7 4 \frac { \log _ { 7 } x } { \log _ { 7 } 4 } l o g 7 4 l o g 7 x E) log ⁡ 7 4 x \log _ { 7 } 4 x lo g 7 4 x

Question

Use the properties of logarithms to condense   log ⁡ 7 x − log ⁡ 7 4 \log _ { 7 } x - \log _ { 7 } 4 lo g 7 ​ x − lo g 7 ​ 4   .A)    log ⁡ 7 ( x − 4 )  \log _ { 7 } ( x - 4 )  lo g 7 ​ ( x − 4 )  B)    log ⁡ 7 x 4 \log _ { 7 } \frac { x } { 4 } lo g 7 ​ 4 x ​ C)    ( log ⁡ 7 x )  1 / 4 \left( \log _ { 7 } x \right)  ^ { 1 / 4 } ( lo g 7 ​ x )  1/4 D)    log ⁡ 7 x log ⁡ 7 4 \frac { \log _ { 7 } x } { \log _ { 7 } 4 } l o g 7 ​ 4 l o g 7 ​ x ​ E)    log ⁡ 7 4 x \log _ { 7 } 4 x lo g 7 ​ 4 x

Ariadna Chacon · Accepted Answer

Final Answer : B, Explanation :   The subtraction of two logarithms with the same base can be condensed into a single logarithm by dividing the arguments, leading to   log ⁡ 7 x 4 \log _ { 7 } \frac { x } { 4 } lo g 7 ​ 4 x ​  .

Use the properties of logarithms to condense $log _ { 7 } x - \log _ { 7 } 4$ .

A) $log _ { 7 } ( x - 4 )$
B) $log⁡7x4\log _ { 7 } \frac { x } { 4 }$
C) $1/4\left( \log _ { 7 } x \right) ^ { 1 / 4 }$
D) $log⁡7xlog⁡74\frac { \log _ { 7 } x } { \log _ { 7 } 4 }$
E) $log _ { 7 } 4 x$

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