Question

Given that

logaN - logax = 3/2
express x in terms of a and N, giving your answer in a form not involving logarithms.

Answer 1

Explanation:

When subtracting logarithms with the same base, it is equivalent to combining them into one logarithm, then dividing the arguments inside:

`log_(a)(n) - log_(a)(x) = log_(a)( (n)/(x) )`

Then use the formula:

`log_(a)( (n)/(x) ) = (3)/(2)`

`{a}^{ (3)/(2) } = (n)/(x)`

`x = n {a}^{ - (3)/(2) }`

Answer 2

N/a^3/2

Explanation:

loga(N/X)=3/2

N/X= a^3/2

X= N/a^3/2