How do I solve for $t$ and $s$ in $y = x^{-t/s}$?

Question

I have $$y = x^{-t/s}$$

How do I solve for $t$ and $s$ in terms of the other variables?

Answer 1

Take the logarithm of both sides of the equation.

$$y = x^{-t/s} \iff \ln y = \ln\Big(x^{-t/s}\Big)$$

Now use a key property of logarithms to extract $-t/s$ from the exponent of $x$: $$\ln(a^b) = b\ln a$$