Question

$log0.01(10000) = x \\ the \: value \: of \: x \: is$
a. 1
b. -2
c. -4
d. 2​

Answer 1

$Given \: log_{0.01} (10000) = x$

/* Exponential form */

$\implies 10000 = (0.01)^{x}$

$\implies (10)^{4} = \big(\frac{1}{10^{2}}\big)^{x}$

$\implies (10)^{4} = (10^{-2})^{x}$

$\implies (10)^{4} = (10)^{-2x}$

$\implies 4 = -2x$

$\implies \frac{4}{-2} = x$

$\implies -2 = x$

Therefore.,

$Option \: \pink { (b) } \: is \: correct.$

•••♪