The equivalent expression to the given logarithm without tables is [tex]\mathbf{ =log_{10} (\dfrac{3x(x^2+4)}{2})}[/tex]. Option A is correct.
What are equivalent expressions?
Equivalent expressions are expressions that differ in appearance but when a value is being replaced for their unknown variable, gives an equivalent result.
From the given information:
[tex]\mathbf{(log_{10}(9)+log_{10}(x) + log_{10}(x^2+4) )-log_{10} (6) }[/tex]
[tex]\mathbf{=log_{10}(9)+log_{10}(x) + log_{10}(x^2+4) -log_{10} (6) }[/tex]
[tex]\mathbf{=log_{10}(9x)+ log_{10}(x^2+4) -log_{10} (6) }[/tex]
[tex]\mathbf{=log_{10}(9x(x^2+4)) -log_{10} (6) }[/tex]
Apply log rule: [tex]\mathbf{log_a(x)-log_a(y) =log_a(\dfrac{x}{y})}[/tex]
[tex]\mathbf{=log_{10}(9x(x^2+4)) -log_{10} (6) =log_{10} (\dfrac{9x(x^2+4)}{6})}[/tex]
[tex]\mathbf{ =log_{10} (\dfrac{9x(x^2+4)}{6})}[/tex]
[tex]\mathbf{ =log_{10} (\dfrac{3x(x^2+4)}{2})}[/tex]
Learn more about equivalent expressions here:
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