Given that $a > 0$, determine which of these expressions is not equivalent to the others - AQA - A-Level Maths Pure - Question 1 - 2019 - Paper 1

Using the power rule of logarithms:

$log₁₀(a²) = 2log₁₀(a)$

This indicates that (log₁₀(a²)) is also equivalent to (2log₁₀(a)).

Using the logarithmic property for square roots, we have:

−4log₁₀(√a) = −4log₁₀(a^{1/2}) = −4×rac{1}{2}log₁₀(a) = −2log₁₀(a)

This implies that (−4log₁₀(√a)) is equivalent to (−2log₁₀(a)).

Thus, the only expression that does not match with others is:

$−4log₁₀(√a)$

Therefore, the answer to circle is (−4log₁₀(√a)).