We can write the log expression in terms of the log of x, y, and z as expression 1/2(logx+2logy-8logz).
What is a logarithm?
It is another way to represent the power of numbers and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.
[tex]\rm a^b = c\\\\log_ac = b[/tex]
We have an expression in logarithm:
[tex]=\rm log\sqrt{\frac{xy^2}{Z^8} }\\\\=log(\frac{xy^2}{Z^8})^{\frac{1}{2} }\\\\=\frac{1}{2}log(\frac{xy^2}{Z^8})[/tex] [tex](\rm loga^b = (b)log(a))[/tex]
[tex]\rm\frac{1}{2} (log(xy^2)-logz^8)[/tex] [tex](\rm log(\frac{a}{b} )= loga - logb)[/tex]
[tex]\rm\frac{1}{2} (log(x)+log(y^2)-logz^8)[/tex] [tex](\rm logab = loga+logb)[/tex]
[tex]\rm\frac{1}{2} (log(x)+2log(y)-8logz)[/tex]
Thus, we can write the log expression in terms of the log of x, y, and z as 1/2(logx+2logy-8logz).
Learn more about the Logarithm here:
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