Aptitude Logarithm Test Paper 311) The value of Log_{10} 2 + 16 log_{10} + 12 log_{10} + 7 log_{10} is
Answer: C Explanation: We know that log m^{n} = n log m So, Log_{10} 2 + log_{10} [2^{4}/ 3*5] ^{16} + log_{10} [5^{2}/ 2^{3} * 3] ^{12} + log_{10} [3^{4}/ 2^{4} * 5] ^{7} Or, log_{10} 2 + log_{10} [2^{64}/ 3^{16} * 5^{16}] + log_{10} [5^{36}/ 2^{36} * 3^{12}] + log_{10} [3^{28}/ 2^{28} * 5^{7}] We know that log m*n = log m + log n Now, log_{10} [2 * 2^{64} * 5^{24} * 3^{28}]/ [3^{16} * 5^{16} * 2^{36} * 3^{12} * 2^{28} * 5^{7}] Or, log_{10} [2^{65} * 3^{28} *5^{24}]/ [2^{64} * 3^{28} *5^{23}] Therefore, log_{10} (2*5) = log_{10} (10) = 1 12) If log (11 + 4√7) = log (2 + x), what is the value of x?
Answer: A Explanation: We have log (11 + 4√7) = log (2 + x) Now, we can write it as log (7 + 4 + 4√7) = log (2 + x) We know that (a+b) ^{2} = a^{2} + b^{2} + 2ab Similarly, log (2 + √7) ^{2} = log(2 + x) Or, log (2 +√7) = log (2 + x) Both side Log will be canceled out Now, 2 + √7 = 2 + x Therefore, x = 2 + √7  2 = √7 13) If log_{10} = 2, find the value of x.
Answer: A Explanation: We have log_{10} = 2 Or, we can write it as log_{10} = 2 log_{10} 10 Or, log_{10} = 2 log_{10} 100 Therefore, both side log will be canceled out. Or, = 4 We know that √x = a, or x^{1/2} = a, then x = a^{2} Similarly, x^{2}  12x + 36 = 4^{2} Or, x^{2}  12x + 36 = 16 Or, x^{2}  12x + 20=0 Now, (x2)(x10) = 0 Or, x2 = 0, and x10 =0 Therefore, we can say that x = 2, x = 10 14) If f(a) = log , f (2a / 1+a^{2}) is equals to
Answer: C Explanation: We can find it by replacing a with Now, f= log Or, log Now, the denominator of both fractions will cancel out each other. Or, log = log We know that log m^{n} = n log m. 15) The value of log_{10}is
Answer: D Explanation: Then the output will be the number itself, i.e., the expressionis equals to 10. Since, log_{m} m = 1 Therefore, log_{10} (10) = 1 Aptitude Logarithm Test Paper 1 Aptitude Logarithm Test Paper 2 Aptitude Logarithm Test Paper 4
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