log _{a} 3=log _{a} frac{1}{3}

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Accepted Answer

Step:1 ：Let (x = log_a 3) and (y = log_a frac{1}{3})Step:2 ：We have (a^x = 3) and (a^y = frac{1}{3})Step:3 ：Since (log_a 3 = log_a frac{1}{3}), we have (x = y)Step:4 ：Now, we can write (a^x = a^y) as (3 = frac{1}{3})Step:5 ：Multiplying both sides by 3, we get (9 = 1)Step:6 ：This is a contradiction, so there is no value of (a) for which (log_a 3 = log_a frac{1}{3})Step:7 ：(boxed{text{No solution}})

Answer

Step: 1 ：Let (x = log_a 3) and (y = log_a frac{1}{3})Step: 2 ：We have (a^x = 3) and (a^y = frac{1}{3})Step: 3 ：Since (log_a 3 = log_a frac{1}{3}), we have (x = y)Step: 4 ：Now, we can write (a^x = a^y) as (3 = frac{1}{3})Step: 5 ：Multiplying both sides by 3, we get (9 = 1)Step: 6 ：This is a contradiction, so there is no value of (a) for which (log_a 3 = log_a frac{1}{3})Step: 7 ：(boxed{text{No solution}})

$\log _{a} 3=\log _{a} \frac{1}{3}$

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