Question

qual o lagaritmo 0,45 no logaritmando 5

Answer 1

$\mathsf{\log_{0,45}{5}}$

$\mathsf{\frac{\log{5}}{\log{0,45}}}$

$\boxed{\mathsf{5\to\frac{10}{2}}}$

$\boxed{\mathsf{0,45\to0,9\cdot0,5\to\frac{9}{10}\cdot\frac{1}{2}\to\frac{3^2}{10}\cdot\frac{1}{2}}}$

$\frac{\log{\frac{10}{2}}}{\log{\frac{3^2}{10\cdot2}}}}}$

$\frac{\log{10}-\log{2}}{2\log{3}-\log{10}-\log{2}}$

$\boxed{\log2\simeq0,301}$
$\boxed{\log3\simeq0,477}$
$\boxed{\log{10}=1}$

$\frac{1-0,301}{2\cdot0,477-1-0,301}$

$\boxed{\frac{0,699}{-0,347}\approx-2,01}$