The required expression for
[tex]log_5(\frac{x}{4} )^2[/tex] = 2 [tex]log_5[/tex] x - 2 [tex]log_5[/tex] 4.
Given,
In the question:
The expression is given as:
Log subscript 5 baseline (startfraction x over 4 endfraction) squared
To find the which expression is equivalent?
Now, According to the question:
The expression is given as:
[tex]log_5(\frac{x}{4} )^2[/tex].
We know that from the properties of logarithm, the following identities
[tex]log m^n = n log m...(1)\\\\log\frac{m}{n} = log m - log n .....(2)[/tex]
Now, [tex]log_5(\frac{x}{4} )^2[/tex] = 2 log [tex]\frac{x}{4}[/tex] (using 1 identity)
Again, Using (2) identity we get,
[tex]log_5(\frac{x}{4} )^2[/tex] = 2 [tex]log_5[/tex] x - 2 [tex]log_5[/tex] 4.
Learn more about Logarithms at:
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