Question 1189078
the expression is:


loga(x^y/z^4)
this becomes:
loga(x^y) - loga(z^4) which becomes:
yloga(x) - 4loga(z)


to confirm this is true, let:
a = 10
y = 5
z = 3
x = 2


loga(x^y/z^4) becomes log(2^5)/3^4) = -.4033350406


yloga(x) - 4loga(z) becomes 5log(2) - 4log3) = -.403335046.


they're the same, confirming the transformation is correct.


not that loga = log10 = log function of your calculator.


also:


log(a/b) = log(a) - log(b)


also:


log(x^a) = alog(x)


here's a reference on log function that might help you to understand.


<a href = "https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/" target = "_blank">https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/</a>


let me know if you have any questions.


theo