For this case we must find an expression equivalent to:
[tex]log_ {5} (\frac {x} {4}) ^ 2[/tex]
So:
We expanded [tex]log_ {5} ((\frac {x} {4}) ^ 2)[/tex]by moving 2 out of the logarithm:
[tex]2log_ {5} (\frac {x} {4})[/tex]
By definition of logarithm properties we have to:
The logarithm of a product is equal to the sum of the logarithms of each factor:
[tex]log (xy) = log (x) + log (y)[/tex]
The logarithm of a division is equal to the difference of logarithms of the numerator and denominator.
[tex]log (\frac {x} {y}) = log (x) -log (y)[/tex]
Then, rewriting the expression:
[tex]2 (log_ {5} (x) -log_ {5} (4))[/tex]
We apply distributive property:
[tex]2log_ {5} (x) -2log_ {5} (4)[/tex]
Answer:
An equivalent expression is:
[tex]2log_ {5} (x) -2log_ {5} (4)[/tex]
