Question

1

Answer 1

The equivalent expression to the given logarithm without tables is $\mathbf{ =log_{10} (\dfrac{3x(x^2+4)}{2})}$. 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:

$\mathbf{(log_{10}(9)+log_{10}(x) + log_{10}(x^2+4) )-log_{10} (6) }$

$\mathbf{=log_{10}(9)+log_{10}(x) + log_{10}(x^2+4) -log_{10} (6) }$

$\mathbf{=log_{10}(9x)+ log_{10}(x^2+4) -log_{10} (6) }$

$\mathbf{=log_{10}(9x(x^2+4)) -log_{10} (6) }$

Apply log rule: $\mathbf{log_a(x)-log_a(y) =log_a(\dfrac{x}{y})}$

$\mathbf{=log_{10}(9x(x^2+4)) -log_{10} (6) =log_{10} (\dfrac{9x(x^2+4)}{6})}$

$\mathbf{ =log_{10} (\dfrac{9x(x^2+4)}{6})}$

$\mathbf{ =log_{10} (\dfrac{3x(x^2+4)}{2})}$

Learn more about equivalent expressions here:

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