Use the properties of logarithms to evaluate log ⁡ 5 75 − log ⁡ 5 3 \log _ { 5 } 75 - \log _ { 5 } 3 lo g 5 75 − lo g 5 3 without a calculator.A) 2B) 1 2 \frac{1}{2} 2 1 C) 72D) log ⁡ 5 75 \log _ { 5 } 75 lo g 5 75 E) None of these

Question

Use the properties of logarithms to evaluate   log ⁡ 5 75 − log ⁡ 5 3 \log _ { 5 } 75 - \log _ { 5 } 3 lo g 5 ​ 75 − lo g 5 ​ 3   without a calculator.A) 2B)    1 2  \frac{1}{2}  2 1 ​ C)  72D)    log ⁡ 5 75 \log _ { 5 } 75 lo g 5 ​ 75 E) None of these

Abdullah Naeem · Accepted Answer

Final Answer : A, Explanation :   log ⁡ 5 75 − log ⁡ 5 3 = log ⁡ 5 75 3 = log ⁡ 5 25 = log ⁡ 5 5 2 = 2 log ⁡ 5 5 = 2 (since  log ⁡ 5 5 = 1 )  \log_5 75 - \log_5 3  & = \log_5 \frac{75}{3}\ & =\log_5 25\ & =\log_5 5^2\ & =2 \log_5 5\ & = 2 \quad 	ext{(since } \log_5 5 = 1 	ext{)}\  lo g 5 ​ 75 − lo g 5 ​ 3 ​ = lo g 5 ​ 3 75 ​ = lo g 5 ​ 25 = lo g 5 ​ 5 2 = 2 lo g 5 ​ 5 = 2 (since  lo g 5 ​ 5 = 1 ) ​

Use the properties of logarithms to evaluate $log _ { 5 } 75 - \log _ { 5 } 3$ without a calculator.

A) 2
B) $\frac{1}{2}$
C) 72
D) $log _ { 5 } 75$
E) None of these

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Use the properties of logarithms to evaluate log⁡575−log⁡53\log _ { 5 } 75 - \log _ { 5 } 3log5​75−log5​3 without a calculator.A) 2B) 12 \frac{1}{2} 21​ C) 72D) log⁡575\log _ { 5 } 75log5​75 E) None of these

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Use the properties of logarithms to evaluate $log _ { 5 } 75 - \log _ { 5 } 3$ without a calculator.

A) 2
B) $\frac{1}{2}$
C) 72
D) $log _ { 5 } 75$
E) None of these