How would you simplify/solve these: 1. log 1/5 125 2. 10 log 17 3. 7^log 7 29 Ho

Question

How would you simplify/solve these: 1. log1/5125 2. 10log 17 3. 7^log729 How would you simplify/solve these: 1. log1/5125 2. 10log 17 3. 7^log729

Explanation / Answer

--> log1/5 125 =    log5 125/ log5 1/5                       = log 53/ log 5-1 ------->here all logsare to the base 5;                       = 3 log5/(-1)log5 ----->again all logs to base 5... it easierfor me to type this way..                       = 3/(-1)    because log5 = log55 as ihave said before...                         =-3 ---> let x = 10log 17       Now log x = log 10log 17= log 17 * log 10 = log 17 * 1 = log 17 log x = log 17, Hence, x = 17,---->this is because log is a one to onefunction....no two values of x can have the same value for logx NOTE: STANDARD FORMULA :    alogab = b ---> 7^log729 = 729; you can work it out the same way we did the previous one, here wehave to take logs to the base 7 that is it!

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