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Example: Find the value of log_{3/4} (243/1024). Solution: Let log_{3/4} (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 = 3^{5} 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 = 2^{10} = (2^{2})^{5} = 4^{5} 243/1024 = 3^{5} / 4^{5} = (3/4)^{5} (3/4)^{x} =(3/4)^{5} Bases are equal so indices are equal. Therefore, x = 5 i.e., log_{3/4} (243/1024) = 5 Directions: Solve the following problems. Also write at least ten examples of your own. 
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