Question 1189078: Express as a sum or difference of logarithms:
1) log a x^y/z^4
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/
let me know if you have any questions.
theo
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