Math  /  Algebra

QuestionFill in the missing values to make the equations true. (a) log35log37=log3\log _{3} 5-\log _{3} 7=\log _{3} \square (b) log25+log2=log245\log _{2} 5+\log _{2} \square=\log _{2} 45 (c) 2log75=log7-2 \log _{7} 5=\log _{7}

Studdy Solution
For part (c), use the power rule of logarithms, which states that alogbM=logb(Ma)a \cdot \log_b M = \log_b (M^a).
Given:
2log75=log7 -2 \log_{7} 5 = \log_{7} \square
Apply the power rule:
log7(52)=log7 \log_{7} (5^{-2}) = \log_{7} \square
Calculate 525^{-2}:
52=152=125 5^{-2} = \frac{1}{5^2} = \frac{1}{25}
Thus, the missing value is:
125 \boxed{\frac{1}{25}}
The solutions for the missing values are: (a) 57\boxed{\frac{5}{7}} (b) 9\boxed{9} (c) 125\boxed{\frac{1}{25}}

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