## Precalculus: Mathematics for Calculus, 7th Edition

$\dfrac{\log{7}}{\log{2}}$
RECALL: The change-of-base formula for loagarithms: $\log_b{x} = \dfrac{\log_a{x}}{\log_a{b}}$ Use the formula above to obtain: $(\log_2{5})(\log_5{7}) = \left(\dfrac{\log{5}}{\log{2}}\right)\left(\dfrac{\log{7}}{\log{5}}\right)$ Cancel common factors to obtain: $\require{cancel}=\left(\dfrac{\cancel{\log{5}}}{\log{2}}\right)\left(\dfrac{\log{7}}{\cancel{\log{5}}}\right) \\=\dfrac{\log{7}}{\log{2}}$