Final answer:
To solve the logarithm equation log(x) 1/729 = -6/5 for the positive solution for x, we can convert it to exponential form. By equating the exponents, we find that x = 243.
Step-by-step explanation:
To solve the logarithm equation, we can convert it to exponential form. Since log base b (x) = y is equivalent to b^y = x, we have 1/729 = x^(-6/5). Taking the reciprocal of both sides gives us 729 = x^(6/5). We can then rewrite 729 as 3^6 and x^(6/5) as (x^(1/5))^6. Equating the exponents, we have 3^6 = (x^(1/5))^6. Taking the fifth root of both sides, we get x^(1/5) = 3. Finally, raising both sides to the fifth power gives us x = 3^5 = 243.