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### High School Mathematics3.5 Problems on Logarithms - IX

 Example: Find the value of log3/4 (243/1024). Solution: Let log3/4 (243/1024) = x Bye definition of logarithm (3/4)x = 243/1024 Factors of 243 = 3*81 = 3 * 3 * 27 = 3 * 3 * 3 * 9 = 3 * 3 * 3 * 3 * 3 243 = 35 Factors of 1024 = 2 * 512 = 2 * 2 * 256 = 2 * 2 * 2 * 128 = 2 * 2 * 2 * 2 * 64 = 2 * 2 * 2 * 2 * 2 * 32 = 2 * 2 * 2 * 2 * 2 * 2 * 16 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 8 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 4 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 1024 = 210 = (22)5 = 45 243/1024 = 35 / 45 = (3/4)5 (3/4)x =(3/4)5 Bases are equal so indices are equal. Therefore, x = 5 i.e., log3/4 (243/1024) = 5 Directions: Solve the following problems. Also write at least ten examples of your own.
 Q 1: Find the value of log5/7 (625/2401).4253 Q 2: Find the value of log3/4 (27/64).5234 Q 3: Find the value of log5/3 (3125/243).2543 Q 4: Find the value of log11/3 (13331/27).5342 Q 5: Find the value of log2/3 (256/6561).8746 Q 6: Find the value of log7/8 (49/64).3452 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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