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

Answer:

N/a^3/2

Step-by-step explanation:

loga(N/X)=3/2

N/X= a^3/2

X= N/a^3/2

Answer 2

Step-by-step explanation:

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

$log_{a}(n) - log_{a}(x) = log_{a}( \frac{n}{x} )$

Then use the formula:

$log_{a}( \frac{n}{x} ) = \frac{3}{2}$

${a}^{ \frac{3}{2} } = \frac{n}{x}$

$x = n {a}^{ - \frac{3}{2} }$