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ext{Log}_{55} rac{11}{44} ext{ if } ext{log}_{55} 44 ext{ is } .861861 ext{ and } ext{log}_{55} 99 ext{ is } 11.365365

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Full solution

Q. ext{Log}_{55} rac{11}{44} ext{ if } ext{log}_{55} 44 ext{ is } .861861 ext{ and } ext{log}_{55} 99 ext{ is } 11.365365
  1. Apply logarithm property: Use the property of logarithms that states log⁡b(1P)=−log⁡bP\log_b (\frac{1}{P}) = -\log_b P.\newlinelog⁡514=−log⁡54\log_5 \frac{1}{4} = -\log_5 4
  2. Substitute given value: Substitute the given value of log⁡54\log_5 4.\newline−log⁡54=−0.861-\log_5 4 = -0.861
  3. Perform calculation: Perform the calculation to find the value.\newline−0.861=−0.861-0.861 = -0.861

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