a^b = 3^3
3^(1/2)^x = a^(1/6)
3^3^x = a
3^3 = a^(1/x)
x = 1/b
Given log(base a)27=b. Find log(base sqrt 3)(a^1/6)
2 answers
Not sure I get this step, since ^ is right-associative:
3^(1/2)^x = a^(1/6)
3^3^x = a
As written, that means 3^(3^x)
I was thinking
(3^(1/2))^x = a^(1/6)
3^(x/2) = a^(1/6)
3^(3x) = a
3^3 = a^(1/x) = a^b
1/x = b
x = 1/b
3^(1/2)^x = a^(1/6)
3^3^x = a
As written, that means 3^(3^x)
I was thinking
(3^(1/2))^x = a^(1/6)
3^(x/2) = a^(1/6)
3^(3x) = a
3^3 = a^(1/x) = a^b
1/x = b
x = 1/b
3 answers