SOLUTION: Express as a sum or difference of logarithms: 1) log a x^y/z^4

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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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