Question

Help me! 1/3^(log1/3 5-3)

Answer 1

1/3^(log1/3 5-3)=5-3=2

Answer 2

Sure, I'd be happy to help you!

To simplify the expression 1/3^(log1/3 5-3), we can use the following properties of logarithms:

1. log_a(b^n) = n * log_a(b)
2. a^log_a(b) = b

Using these properties, we can rewrite the expression as follows:

1/3^(log1/3 5-3) = 1/3^[(log(5)/log(1/3))-3] (since log1/3 5 = log(5)/log(1/3))

= 1/3^[(log(5)/log(1/3)) - (3 * log(1/3)/log(1/3))] (since 3 = 3 * log(1/3)/log(1/3))

= 1/3^[(log(5) + 3 * log(1/3))/log(1/3)]

= 1/3^[(log(5) - log(1/3^3))/log(1/3)]

= 1/3^[(log(5) - log(27))/log(1/3)]

= 1/3^[(log(5/27))/log(1/3)]

= 1/(3^(log(5/27))/log(1/3))

= 1/[(1/3)^(log(5/27))]

= (3^(log(5/27)))^-1

= (5/27)^(-log(3)/log(5))

= (27/5)^(log(3)/log(5))

Therefore, the simplified expression is (27/5)^(log(3)/log(5)).

I hope that helps! Let me know if you have any questions.