CAT Logarithms previous year questions

14 Logarithms questions from CAT 2021–2025 (Quant), each with its answer and a step-by-step solution.

• Q3The number of distinct integers n for which log_(1)/(4) (n²-7n+11 )>0 , isCAT 2025 Slot 1 · Quant · Logarithms
• Q2If log_64x²+log_8√y+3log_512 ( √y z )=4 , where x , y and z are positive real numbers, then the minimum possible value…CAT 2025 Slot 2 · Quant · Logarithms
• Q7The sum of all possible real values of x for which log_x-3 (x²-9 )=log_x-3 ( x+1 )+2 , isCAT 2025 Slot 3 · Quant · Logarithms
• Q22If x is a positive real number such that 4log_10x+4log_100x+8log_1000x=13 , then the greatest integer not exceeding x…CAT 2024 Slot 1 · Quant · Logarithms
• Q9If a , b and c are positive real numbers such that a>10≥ b≥ c and (log_8 ( a+b ))/(log_2c)+(log_27 ( a-b…CAT 2024 Slot 2 · Quant · Logarithms
• Q16If 3^(a)=4 , 4^(b)=5 , 5^(c)=6 , 6^(d)=7 , 7^(e)=8 and 8^(f)=9 , then the value of the product abcdef isCAT 2024 Slot 3 · Quant · Logarithms
• Q22The sum of all distinct real values of x that satisfy the equation 10^(x)+(4)/(10^(x))=(17)/(2) , isCAT 2024 Slot 3 · Quant · Logarithms
• Q1If x and y are positive real numbers such that log_x (x²+12 )=4 and 3log_yx=1 , then x+y equalsCAT 2023 Slot 1 · Quant · Logarithms
• Q5For some positive real number x , if log_√3 ( x )+(log_x ( 25 ))/(log_x ( 0.008 ))=(16)/(3) , then the value of log_3…CAT 2023 Slot 2 · Quant · Logarithms
• Q1For a real number x , if (1)/(2) , (log_3 (2^(x)-9 ))/(log_34) , and (log_5 (2^(x)+(17)/(2) ))/(log_54) are in an…CAT 2023 Slot 3 · Quant · Logarithms
• Q14The number of distinct integer values of n satisfying (4-log_2n)/(3-log_4n)<0 , isCAT 2022 Slot 2 · Quant · Logarithms
• Q18If 5-log_10√(1+x)+4log_10√(1-x)=log_10(1)/(√(1-x²)) , then 100x equalsCAT 2021 Slot 1 · Quant · Logarithms
• Q2If log_2 [ 3+log_3\4+log_4 ( x-1 )\ ]-2=0 then 4x equalsCAT 2021 Slot 2 · Quant · Logarithms
• Q6For a real number a , if (log_15a+log_32a)/( (log_15a ) (log_32a ))=4 then a must lie in the rangeCAT 2021 Slot 3 · Quant · Logarithms